Cut the prosciutto in 4 crosswise. Fold over each slice and spread out on a work surface.
In a bowl, gently toss the cherry tomatoes with olive oil. Season with salt and pepper.
Garnish each slice of prosciutto with a tomato half, a basil leaf, and a cheese stick.
Roll up and secure with a toothpick, transfer to a serving platter and season with fresh ground black pepper to taste.
