How to cook bell peppers until they are VERY tender, but not broken down?
I'm not sure that this is how the restaurant did it, but perhaps that kind of texture could be achieved by blanching and freezing the pepper pieces, then reheating them in a microwave just prior to adding them to the sauce and serving. Blanching would ensure that they don't taste completely raw, and freezing would make them "mushier" without ruining the shape by extended cooking.

I haven't tried this myself, so no guarantees.