Heat the oven to 350°F and butter a 9-by-13-inch baking dish. Spread the croissant pieces on a baking sheet and toast for 8 minutes to dry their cut surfaces.
Cut the drained peppers into short strips. Arrange the croissants, peppers and goat cheese in the baking dish.
Whisk the eggs, milk, mustard, salt and pepper. Pour over the croissants and gently press the lower pieces into the liquid; let stand for 10 minutes.
Bake uncovered for 30 to 35 minutes, tenting with foil if the pastry tips darken early, until the center custard reaches 160°F.
Rest for 10 minutes and serve with a broad spoon so each portion includes both a crisp top and a soft center.