Step 1

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.

Step 2

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 (save remaining peppers and their juices for another use; we love them tossed with pasta, layered into sandwiches, or stirred into frittatas). Add vinegar; season with salt. Stir to combine, then drizzle dressing over salad.

Step 3

Do Ahead: Peppers can be roasted 1 week ahead. Cover and chill.