To make the vinaigrette. Combine 1/4 cup olive oil, the honey, pistachios, lemon juice, vinegar, basil, chives, thyme, garlic, and a pinch each of salt, pepper, and chili flakes in a glass jar and whisk until smooth. Taste and adjust the salt and pepper.
Preheat the grill or grill pan to high.
In a large bowl, toss the peppers & tomatoes with 2 tablespoon olive oil, paprika, chili powder, salt and pepper. Place the bread on a baking sheet and drizzle with olive oil on both sides of each slice, season with salt.
Place the bread on the grill and grill both for about 2-3 minutes per side or until lightly toasted. Remove from the grill. At the same time, grill the peppers until softened and charred, 3-4 minutes per side. Remove from the grill and arrange on a serving plate.
Drizzle the vinaigrette over the peppers & tomatoes , then break the balls of burrata around the peppers. Let everything sit 5-10 minutes. Serve with vinaigrette and grilled bread.