Oh I have the cure thats for sure!
You need to replace your
power brake booster.
There is a diaphragm inside the brake booster that warps after time and in colder weather (like mornings) when you hit the brake pedal it flexes the diaphragm and creates a vacuum leak causing the stall.
You can test this by bypassing the brake booster in the morning by disconnecting the big hose coming off of it and plugging it with something (I used a sharpie, it fit perfectly), then doing a reverse to drive thing in your driveway and seeing that it will not stall out. Just be careful when testing that in that fashion as you do not have brakes really. Do it in a controlled place, where no one can get hurt.
I replaced mine and the issue went away instantly. That took me a ton of troubleshooting to figure that out, but yes, that is whats wrong. Its a vacuum leak from within the power brake booster. Any questions along the way, just ask! I had a ton of people help me out and i'll be glad to pay it forward.