Preheat oven to 425F. In a large baking dish, toss tomatoes with olive oil, basil, oregano, salt, pepper, and red pepper flakes.
Spread tomatoes into an even layer in the dish, leaving a small space in the center for the goat cheese. Add goat cheese and bake, uncovered, for 20 minutes.
While the dish is baking, boil your pasta in salted water according to package directions. I add about 1 tbsp salt to my boiling water.
Before you drain the pasta, reserve 1/2 cup of the cooking water and set aside.
Remove dish from oven. Add in garlic and spinach. Drizzle about 1/4 cup of the pasta water over the spinach and toss all ingredients together until spinach begins to wilt, cheese melts in the tomatoes, and a thick sauce forms.
Toss in cooked and drained pasta. Add in more pasta water as needed to thin the sauce. Serve.