Combine basil leaves, pine nuts, garlic, 1/3 cup parmesan cheese, olive oil and a pinch salt in a food processor. Puree until almost smooth.
Preheat the oven to 400 degrees F. Lightly spray a 12-cup muffin tin with nonstick cooking spray.
To make meatballs:
In a large bowl, mix to combine breadcrumbs and milk. Add the ground beef, parsley, Italian seasoning, grated parmesan cheese, egg, salt and pepper. Divide into 12 equal balls. Flatten into patties and place a mozzarella cube in the center, then close the meat around to make a ball.
Heat oil in a large skillet over medium. Working in batches if necessary, brown the meatballs, about 2 minutes per side. Remove from skillet and seat aside on a plate.
To make spaghetti cups, combine cooked spaghetti with 1/2 cup pesto, 2 beaten eggs, 1/4 cup grated parmesan cheese and 1 cup grated mozzarella. Divide spaghetti into prepared muffin tin and make a well in the center of each.
Place a meatball in the center of each spaghetti nest. Top with 2 teaspoons of grated mozzarella cheese. Bake for 15 minutes until the meatballs are cooked through.