How to Make It
Preheat the oven to 500°. On a baking sheet, lightly rub the bell peppers with vegetable oil. Roast for about 20 minutes, turning the peppers halfway through, until blackened in spots. Transfer the peppers to a bowl, cover with plastic and let cool. Peel the peppers and cut them lengthwise into thirds; discard the stems, cores and seeds.
In a small bowl, combine the parsley with the capers, olive oil and garlic and season lightly with salt and pepper. Spread the peppers on a work surface. Lay the mozzarella sticks on the short ends and top with the anchovies. Spoon the parsley mixture on top and roll into tight cylinders. Trim the ends and cut the rolls in half. Skewer with toothpicks and serve.
Make Ahead: The rolls can be kept at room temperature for up to 4 hours or refrigerated for up to 8 hours. Bring to room temperature before serving.