Preheat oven to 325°. Toss peppers, chiles, garlic, and oil in a Dutch oven or heavy roasting pan; season with salt and pepper and toss again to coat.
Cover and roast, tossing occasionally, until peppers are very tender, 2–2½ hours. Let cool.
Arrange half of peppers on a platter. Top peppers with mozzarella and basil.
Measure out 3 Tbsp. of the oily juices left behind and transfer to a small bowl
Add vinegar; season with salt. Stir to combine, then drizzle dressing over salad.
You can eat cold or hot. Bon Appetit.