Broad struck five times in his first four overs, claiming his 300th test victim with the third ball of the match when he had opener Chris Rogers caught at first slip by captain Alastair Cook for a duck.
"It was just one of those days you dream of, to take your 300th wicket on your home ground," Broad told reporters.
"It was a freak day but it's what you work hard for."
Steven Smith, on six, edged the last ball of the first over to Joe Root in the slips.
Shaun Marsh edged Broad to Ian Bell at second slip and Adam Voges was brilliantly caught one-handed by a diving Ben Stokes at gully.
Michael Clarke drove at a wide ball from Broad and was well caught above his head by Cook to give the bowler his 14th five-wicket haul tests.
"The pitch offered the perfect amount of movement and we took some amazing catches," Broad said. "Stokesy's was one of the best I've ever seen."
Broad, playing his 83rd test, became the fifth England bowler to take 300 test wickets after fellow pacemen James Anderson, Ian Botham, Bob Willis and Fred Trueman.
"It's nice to get to the milestone and join those great England bowlers," said Broad who also dismissed Mitchell Starc, Mitchell Johnson and Nathan Lyon in an inspired display.
"It was definitely the perfect all-round bowling and fielding performance by us," the 29-year-old said.
Broad left the field clutching the ball to a standing ovation before putting his feet up to watch England pile up 274 for four and build a lead of 214 runs, a commanding position from which to secure the victory that would seal the Ashes.
"It's the best day's cricket I have been involved in," Broad said. "To bowl out a team like Australia for 60 and then score 270-odd was an amazing achievement.
"We know Australia will fight back but we want to bat them out of the game now."
