Position a rack in the middle of the oven; preheat to 400 degrees . Divide the salami between two 12-cup muffin pans, pressing the salami slices into the cups.
Tear aluminum foil into pieces; lightly mold into twenty-four 1-inch balls. Push the foil balls into each muffin cup to secure the salami. Bake until the salami is crisp, about 15 minutes. Remove from the oven; let cool slightly in the pan. Discard the foil.
In a medium bowl, mix the artichoke hearts, roasted peppers, 1/4 cup basil and the mozzarella balls.
Place the salami cups on a platter. Fill with the vegetable mixture. Top with more chopped basil.