Welch, a 40-year-old from Washington in northeast England, was working for the National Health Service when she began her refereeing career in 2010.
She rose through the officiating ranks and, in 2021, became the first woman appointed to referee a match in the English Football League when she took charge of the fourth-tier fixture between Harrogateand Port Vale.
Welch was also the first female official to referee matches in the Championship and third round of the FA Cup. Kompany, who spoke to Welch after full-time at Craven Cottage, said: "I wanted to congratulate her because it's a big moment.
"After the game it's fair to say that it's a milestone moment and may there be more, and the best thing will always be when someone is judged on merit. But you have to have a first and this is it, so well done (to her) and I'm happy to be part of this moment."
Welch had little to do early on during a slow start in London on Saturday before her decision to not award a Vitinho handball frustrated Fulham.
Welch remained unmoved by players' reactions when making her rulings and was happy to play advantage for both sides whenever possible in a match in which long-range strikes from Wilson Odobert and Sander Berge gave Burnley only their third league win of the season.
She booked Calvin Bassey after 25 minutes for striking Josh Brownhill. The Fulham defender refused to walk towards Welch when signalled by her on three occasions but eventually approached the referee and was cautioned.
Welch's name was greeted by cheers when read out by the public address announcer at Craven Cottage ahead of kick-off. But Fulham fans became increasingly annoyed as Welch's first few decisions went in favour of the visitors and they cheered sarcastically when the
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