Preheat your oven for 350°F.
In a 9x13 inch baking dish, combine cherry tomatoes, garlic, thyme, salt and black pepper (reserve a small pinch of each for the feta), and about half of your olive oil. Give it a toss to combine and flatten the tomatoes into one even layer.
Create an empty spot in the middle of the baking dish and place your feta in the center space. Top the feta with the remaining oil, salt and pepper.
Bake the tomato and feta mix in the center of your preheated 350°F oven for 40 to 50 minutes, or until the tomatoes and feta have softened and the tomatoes start to burst.
While it bakes, bring a large pot of salted water to a boil. Add in your pasta, and cook according to the package instructions. Drain and set aside while you wait for the feta and tomatoes to finish baking.
Once the feta and tomatoes have finished baking, give them a mash with a fork to break everything up. Add your pasta to the baking dish and mix it in with the sauce. (Optional) Top with parsley. Serve!