Preheat the oven to 400°F. Set a big pot of salted water to boil.
In an oven-safe dish (about the size of 13x9-inch baking dish), add the spinach and garlic cloves.Stir in the cherry tomatoes, 2 tablespoons olive oil, salt and ½ teaspoon black pepper. Add thyme sprigs.
Push the tomatoes to the sides of the dish and then place the block of feta cheese in the center. Drizzle the remaining 1 tablespoon olive oil on top of the feta and crack some fresh black pepper on it.
Place the dish in the oven and bake until the cheese has softened and the tomatoes are roasted, about 25 minutes.
Add your to the pot of salted boiling water and cook until al dente, about 10 minutes. Drain the pasta and set it aside.
Take the dish out of the oven. Strip the thyme leaves off of the sprigs using a fork, Using the same fork, mash and mix everything together to make a “sauce”. Add the drained pasta to the sauce, mix and enjoy!