Preheat oven to 350° F.
Lightly spray a rimmed baking sheet with cooking spray and set aside.
Bring a medium-large pot of salted water to a boil. Add all pasta nests and then turn heat down so the water is only gently bubbling, and cook for 2 minutes, just until al dente. Using a slotted spoon, quickly remove pasta nests from water, draining away as much water as you can, and place them on prepared rimmed baking sheet. Set aside. Do not discard pasta water.
Heat 12″ cast iron skillet or other 12″ oven-safe skillet over medium to medium-low heat. Add butter. Once melted, add garlic, stirring to coat. Sauté for about 3 minutes, stirring regularly, until garlic is softened. If garlic starts to brown, turn heat down a bit. Stir in cream and kosher salt. When mixture starts to bubble, let simmer for 2 minutes longer, stirring every now and then. Add 2 tablespoons of the reserved pasta water, and then whisk in grated Parmesan until smooth. Taste test and add a bit more salt, if needed. Remove skillet from heat. Nestle each of the cooked pasta nests into the cream sauce. Add 1 teaspoon of pesto to the centers of each pasta nest, spreading out the pesto into the pasta a bit. Press a chicken meatball into the center of each pasta nest and then add a bit more pesto to the top of each meatball. Cover skillet with foil, aiming to not let the foil touch the meatballs, and place in oven. Bake for 20 to 25 minutes, or until cream sauce is bubbling lightly. Sprinkle each pasta nest with a bit of freshly ground black pepper, plus freshly shredded Parmesan, minced parsley, and basil leaves, if desired. Serve hot.
