How to Make It
Preheat grill to medium (350°F to 400°F). Trim and discard tops and bottoms from bell peppers; remove and discard seeds and white membranes using a paring knife. Slice each bell pepper in half lengthwise. Brush evenly with 2 tablespoons of the oil. Place bell peppers, skin sides down, on oiled grates. Grill, uncovered, until charred, about 7 minutes. Turn bell peppers; grill until tender, about 5 minutes. Transfer to a large heavy-duty ziplock plastic bag. Seal and let stand 10 minutes.
Remove bell peppers from bag. Remove and discard skins. Chop bell peppers into ¾- to 1-inch pieces. Transfer to a serving platter, and sprinkle with salt and black pepper. Top peppers with mozzarella, and drizzle with lime juice and remaining 2 tablespoons oil. Sprinkle with basil before serving.