The Dodgers did a few things.
I was going to do a long stat filled post, but the short story is that Brasier's 4 seam fastball is awful(.389 wOBA in 2022). Even so, Boston had him using it more than any other pitch despite the fact that he actually had a dominant slider. When he went to LA, they drastically reduced how often he threw that 4 seam and incorporated a cutter which also became a dominant pitch. This gave him 2 dominant offerings and he could use the 4 seam to keep batters honest. So yes, the cutter was huge for him, but Boston used him entirely wrong as well. Correcting both of those things turned him into the dominant reliever that posted a .70 ERA and 2.48 FIP in his 38 2/3 innings with the Dodgers. He likely isn't sniffing that ERA again, but there's nothing to suggest that he isn't a guy who could post a sub 3.00 ERA again which is why there's so many teams in on him. I'm actually quite interested in him now even if it's a multi year deal.