I have worked on cars - I am guessing it is a brake control unit. That is a computer, and it is quite expensive to replace as it controls how the brakes work (all those fancy features like ABS, Traction Control, etc.) Those can easily run you over $1000 to fix as the part is nearly that on its own without figuring in the labor to replace and ensure the programming is okay. Figure another $400 in labor (about four hours or half a day of work so that $1800 is an honest estimate for something like that part).
I would believe your mechanic and not deal with it. I am only guessing and that is all any of us can do as you don't know the name of the component that is broken.