Place both whole spaghetti squash in a large stockpot, and cover with 2 inches of water. Cover and bring the water to a boil. Reduce heat to a simmer, and cook the squash until it is slightly tender when you press it with your fingers, 20 to 30 minutes. Drain. Using a serrated knife, cut the squash in half crosswise. Stand the halves on end, with cut-sides up, and set aside to cool 15 minutes.
Preheat the oven to 450 degrees. Remove seeds from squash halves; discard. Using a fork, scrape the flesh; it will separate into spaghetti-like strands. Transfer the strands to a mixing bowl, and transfer squash shells to a baking pan; set both aside.
Chop 12 tomatoes into 1/2-inch pieces; add to squash. Slice remaining 4 tomatoes into 1/4-inch-thick rounds; set aside.
Place the garlic, olive oil, basil leaves, salt, and pepper in the bowl of a food processor. Process until the basil has been very finely chopped, about 2 minutes.
Transfer the basil mixture to the mixing bowl with the squash strands and the tomato pieces; toss with the vegetables to combine. Divide the mixture among the reserved squash shells, and top each shell with several tomato slices. Sprinkle 1 1/2 tablespoons of the Parmesan cheese over each shell.
Transfer pan to the oven; bake the stuffed squash until the cheese is golden and a metal skewer inserted down into the stuffing comes out hot when held there for 15 seconds, about 30 minutes. Garnish with the basil sprigs. Serve hot.