Position a rack in the center of the oven and preheat to 425º. Add bell peppers, gnocchi, and garlic to a large sheet pan and toss to coat with 2 tablespoons oil, salt and pepper to taste, and red pepper flakes.
Roast for 30 minutes, tossing halfway through, until peppers are totally softened and gnocchi have started to brown.
Top with burrata and basil and drizzle with remaining 1 tablespoon oil and balsamic glaze.
