I've been dealing with this problem for a while. I start my truck and it runs great. Has 180 original miles on the motor with new head gaskets about 6 months ago.
Once I hit the brakes it stumbles and just putters. Most of the time it will die. I replaced rear brakes first with no luck. This last week I bought a brand new master cylinder and booster combo from the local auto parts store and put that on. I bled the brakes and still no luck.
I'm thinking it has to be some type of Vaccume problem? I know I shouldn't have thrown parts at it but hey, at least now I have a new set up up top. It seems like I can get the rough idle to go away after a little while if I keep restarting it after it dies and messing with the pedal.. The brakes actually work well as far as stopping goes, but not excellent. they feel a bit spongy sometimes too.

Any help would make me feel much better! Thank you
Kenny

 

Wonder if you have a vacuum leak at the brake booster.