01 - Preheat oven to 400°F.
02 - Combine halved cherry tomatoes, sliced sun-dried tomatoes, garlic, and 2 tablespoons olive oil in a large ovenproof baking dish. Season with salt, pepper, oregano, and red pepper flakes as desired. Toss ingredients thoroughly.
03 - Place the feta block in the center of the baking dish, nestled among the tomatoes. Drizzle remaining 1 tablespoon olive oil over the cheese and season lightly with black pepper.
04 - Bake for 25 to 30 minutes until tomatoes have burst and feta is softened with browned edges.
05 - While baking, add 1 tablespoon olive oil to a skillet set over medium heat. Cook sliced onions, stirring occasionally, for 15 to 20 minutes until deeply golden and caramelized. Set aside.
06 - While onions cook, prepare pasta in a large pot of boiling salted water according to package instructions until al dente. Reserve 1/2 cup pasta cooking water, then drain pasta.
07 - After baking, remove dish from oven. Add caramelized onions and chopped basil to the baking dish. Stir thoroughly, breaking the feta until it forms a creamy sauce.
08 - Add drained pasta to the baking dish. Toss gently to coat pasta evenly in sauce. Incorporate reserved pasta water, a little at a time, to reach preferred sauce consistency.
09 - Serve immediately, finishing with extra basil and a drizzle of olive oil, if desired.