Heat oven to 350°F; butter 9-by-13-inch dish. Toast croissant pieces on sheet 8 minutes to dry cut surfaces.
Cut drained peppers into short strips. Arrange croissants, peppers, and goat cheese in dish.
Whisk eggs, milk, mustard, salt, and pepper; pour over croissants. Gently press lower pieces into liquid; stand 10 minutes.
Bake uncovered 30 to 35 minutes to 160°F in center custard, foil-tenting if pastry tips darken early.
Rest 10 minutes; serve with broad spoon, including crisp top and soft center in each portion.