Preheat the oven to 400 F. Add the cherry tomatoes to a 9x13 inch baking dish and toss with most of the olive oil, the salt and the black pepper.
Place the dairy free feta block in the center of the dish, push the tomatoes around it, and drizzle the remaining olive oil over the top of the feta.
Bake for 30-35 minutes until the tomatoes have burst and the feta is very soft with golden edges.
While the dish bakes, cook the rigatoni in salted boiling water until al dente. Reserve 3/4 cup of the pasta water before draining.
As soon as the dish comes out of the oven, stir the garlic and red pepper flakes into the hot tomatoes and feta. Mash everything together with a fork until it turns into a creamy sauce.
Add the rigatoni and a splash of the reserved pasta water, tossing until the sauce is glossy and coats the pasta. Top with fresh basil and serve immediately.