For the basil puree, place the basil leaves, garlic, shallot and a pinch of salt and pepper into a food processor. Process the mixture by pulsing a few times to begin grinding up the ingredients. Add the oil slowly as the processor runs to emulsify the sauce. Add more salt and pepper to taste, and then set aside.
Preheat the grill on medium-high heat.
Thread 4 Grilled Nuggets, 2 tomatoes and 1 mozzarella ball onto each skewer, alternating for the best color combination.
Quickly grill the skewers for about 30 seconds on each side to warm the tomato and cheese. Place on serving plates or family-style platters.