After defeating League Two rivals Chesterfield in round two, Peschisolido wanted to be drawn against one of the Premier League`s big teams.
Albion were paired with Boro and the Championship club will visit the Pirelli Stadium over the weekend of January 8-9.
Peschisolido said: "For me, it's a very glamorous side to be drawn against. They'd been known as a Premier League side for a long time, and it was only two seasons ago that they were there.
"There's two divisions between us though, so it will be tough."
Source: PA
Source: PA