Wash the bell peppers thoroughly and pat them dry. Slice each pepper in half lengthwise and remove most of the seeds and membranes. Lightly coat them with olive oil and season generously with salt and pepper.
In a small bowl, combine red wine vinegar, minced garlic, crushed red pepper flakes, salt, and pepper. Slowly whisk in the olive oil until the dressing becomes smooth and emulsified. Set aside for later use.
Heat a skillet over medium heat and melt the butter. Add the torn sourdough pieces along with garlic powder, salt, and pepper. Stir frequently until the crumbs become golden brown and crisp.
Preheat the grill to medium-high heat. Place the peppers cut-side down on the grill and cook until lightly charred and softened. Flip them and continue grilling until tender but still slightly firm.
Transfer the grilled peppers to a serving platter. Drizzle some of the prepared vinaigrette over the warm peppers and allow them to rest for several minutes. This helps them absorb all the delicious flavors.
Gently tear the burrata into pieces and place it over the marinated peppers. The creamy cheese melts slightly against the warm peppers, creating an incredible texture contrast.
Scatter the crunchy breadcrumbs over the top of the burrata and peppers. Finish with fresh herbs and another light drizzle of vinaigrette. Serve immediately while the peppers are still slightly warm.