Preheat your grill or grill pan over medium-high heat.
Slice each bell pepper in half lengthwise and remove the seeds and membranes.
In a mixing bowl, toss the torn sourdough pieces with 2 tablespoons of olive oil, minced garlic, salt, and black pepper until evenly coated.
Place the peppers cut-side down on the hot grill or grill pan. Grill for about 5-7 minutes until the skin is charred and the peppers are tender.
While the peppers are grilling, spread the sourdough mixture on a baking sheet and toast in the oven at 375°F (190°C) for about 8-10 minutes, or until crispy and golden brown. Stir occasionally to ensure even toasting.
Once the peppers are cooked, remove them from the grill and place them on a serving platter, cut side up.
Tear or slice the burrata cheese and place it generously on top of each grilled pepper half.
Sprinkle the toasted sourdough breadcrumbs over the burrata.
Drizzle with the remaining tablespoon of olive oil and balsamic glaze (if using) for extra flavor.
Garnish with fresh basil leaves if desired and serve immediately.