The market, which is expected to post over Dh100 billion in sales through more than 30,000 transactions in first quarter, will sustain steady increase in transactions and prices throughout the year
England had slumped to 280-8 after losing four wickets for 18 runs before No 10 Broad's swashbuckling 62 took them to a first-innings total of 369.
When bad light forced an early close, the West Indies were 232 runs behind, needing 33 more to avoid the follow-on.
West Indies captain Jason Holder was 24 not out and Shane Dowrich 10 not out.
The veteran new-ball duo of Broad and James Anderson, paired together for the first time this series, both had stumps figures of 2-17.
"We were hoping to get 400 at the start of the day, that was our plan, but we're happy with getting over 350," Broad told Sky Sports.
"With our discipline with the ball, we've had a great day," he added, with England looking to win this three-match series 2-1 and regain the Wisden Trophy.
West Indies fast bowler Kemar Roach, who earlier took his 200th Test wicket in a return of 4-72, admitted his side were in a tough spot.
"We started well but Stuart Broad came in and played his shots and things went his way," Roach told the BBC.
"Things drifted a bit and we're in a difficult position now but the guys will fight it out."
Broad struck with just his fourth ball to have West Indies dangerman Kraigg Brathwaite caught at slip by England captain Joe Root for one.
John Campbell, dropped on 10 by normally reliable second slip Ben Stokes, looked increasingly assured while making 32.
But fast bowler Jofra Archer, back after being omitted from England's 113-run win in the second Test for breaching the bio-secure regulations governing this series, produced a rib-high delivery that left-hander Campbell could only fend to gully.
Anderson, England's all-time leading Test wicket-taker, then struck either side of tea on his Lancashire home ground as the tourists declined to 59-4.
The struggling Shai Hope was caught behind for 17 after being squared up by a full-length Anderson delivery that moved away late - a desperately difficult ball to play.
Anderson then had Shamarh Brooks inside edging to wicketkeeper Jos Buttler with one that cut the other way.
In a campaign that marks international cricket's return from lockdown, Broad's classic nip-backer had Roston Chase lbw to the leave the West Indies in dire straits at 73-5.
Jermaine Blackwood, who made a match-clinching 95 in the West Indies' four-wicket win in the first Test, looked good during his 26.
But Blackwood was bowled between bat and pad by Chris Woakes to give all of England's pace quartet a wicket, with Stokes unable to bowl because of a quad injury.
Dowrich was lucky when he got in a tangle against an Archer bouncer, only for the ball to just clear the back-pedalling Rory Burns in the gully.
England resumed on 258-4 after losing the toss.
Ollie Pope was 91 not out and Buttler unbeaten on 56 - his first Test fifty in 14 innings.
Pope, however, failed to add to his score.
In sight of his second Test century, Pope had already been dropped by Rahkeem Cornwall in the slips when Shannon Gabriel clean bowled him to end a fifth-wicket stand of 140.
Buttler was well caught low down for 67 by Holder at second slip.
But Broad, who has a highest Test score of 169, counter-attacked with his first fifty at this level in just over three years.
On a ground where he was hit on the face by a bouncer from India's Varun Aaron in 2014, left-handed batsman Broad pulled Roach for six as the new ball started to soften.
Broad completed a 33-ball fifty before hitting a full-toss from occasional off-spinner Chase to deep midwicket.
R. Burns c Cornwall b Chase 57
D. Sibley lbw b Roach 0
J. Root run out (Chase) 17
B. Stokes b Roach 20
O. Pope b Gabriel 91
J. Buttler c Holder b Gabriel 67
C. Woakes b Roach 1
D. Bess not out 18
J. Archer c Holder b Roach 3
S. Broad c Blackwood b Chase 62
J. Anderson c Cornwall b Holder 11
Extras (b12, lb4, nb6) 22
Total (all out, 111.5 overs, 494 mins) 369
Fall of wickets: 1-1 (Sibley), 2-47 (Root), 3-92 (Stokes), 4-122 (Burns), 5-262 (Pope), 6-267 (Woakes), 7-272 (Buttler), 8-280 (Archer), 9-356 (Broad), 10-369 (Anderson)
Bowling: Roach 25.4-4-72-4; Gabriel 23.2-5-77-2 (5nb); Holder 24.5-5-83-1 (1nb); Cornwall 27-5-85-0; Chase 11-3-36-2
West Indies 1st Innings
K. Brathwaite c Root b Broad 1
J. Campbell c Burns b Archer 32
S. Hope c Buttler b Anderson 17
S. Brooks c Buttler b Anderson 4
R. Chase lbw b Broad 9
J. Blackwood b Woakes 26
J. Holder not out 24
S. Dowrich not out 10
Extras (b4, lb5, w5) 14
Total (6 wkts, 47.1 overs, 229 mins) 137
To bat: R Cornwall, K Roach, S Gabriel
Fall of wickets: 1-1 (Brathwaite), 2-44 (Campbell), 3-58 (Hope), 4-59 (Brooks), 5-73 (Chase), 6-110 (Blackwood)
Bowling: Anderson 11-4-17-2; Broad 10-3-17-2; Archer 13.1-1-55-1 (5w); Woakes 13-1-39-1;
Match position: West Indies are 232 runs behind with four first-innings wickets standing
Toss: West Indies
Umpires: Michael Gough (ENG), Richard Kettleborough (ENG)
TV umpire: Richard Illingworth (ENG)
Match referee: Chris Broad (ENG)
The market, which is expected to post over Dh100 billion in sales through more than 30,000 transactions in first quarter, will sustain steady increase in transactions and prices throughout the year
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