Preheat oven to 425 degrees F.: You will notice the oven building dry heat, which encourages the tomatoes to blister rather than steam, creating concentrated sweetness and caramelized edges. Getting the oven to a true 425 degrees matters because a lower temperature yields a softer roast and less pop from the skins; use an oven thermometer if yours runs cool. A common error is placing the dish in before the oven is hot, which prolongs roasting time and can underdevelop flavor.
Add the tomatoes, sun-dried tomatoes, pesto, olive oil, oregano, parsley, salt, pepper, thyme and red pepper flakes. Stir all of the ingredients together until evenly coated.: As you mix, you will see the tomatoes glisten with olive oil and the herbs speckle the surface. The scents of herbaceous pesto and fruity oil rise up, hinting at the roast to come. Ensuring each tomato is coated promotes even roasting and prevents any from drying out. Avoid overcrowding the pan, because crowded tomatoes steam instead of roast.
Make room in the center of the dish and add the feta. Drizzle the top of the feta with olive oil.: The block should sit exposed so it takes on heat directly while the surrounding tomatoes burst. Drizzling olive oil over the feta encourages browning at the edges and keeps the cheese moist. If you bury the cheese, it will not soften uniformly, so leave it centered and exposed.
Bake uncovered for 35 minutes or until the until the feta is soft and tomatoes are bursting.: You will hear occasional pops as the cherry tomatoes split and their juices release, and the feta will collapse slightly and look pillowy. Visual cues matter more than a strict timer here, so aim for wrinkled tomato skins and a soft, pressable cheese. If the top seems to brown too quickly, tent with foil to prevent burning while the center finishes.
Meanwhile, chop the garlic and basil and cook the pasta in salted water according to the package directions (plan on adding the pasta to the boiling water 10 minutes before the feta and tomatoes are done). Before draining the pasta, reserve 1 cup of the pasta cooking water for later.: Boiling water should have a lively rolling boil, and the salted water seasons the pasta from within. The reserved cooking water holds starch that helps emulsify the sauce, giving it a glossy, silky texture. A mistake is not reserving water, which can make the sauce cling poorly or seem dry when tossed.
Remove the dish from the oven and immediately add the garlic and basil and stir for 30 seconds so the residual heat can cook the garlic.: The pan will be steaming hot, and stirring right away allows the garlic to release fragrance without becoming raw. You should smell a bright, aromatic note, and the basil will wilt but stay vibrant. Avoid letting the garlic sit in the hot dish too long, as it can become bitter if it overcooks.
Using a spatula, press down on the feta cheese to break it down and make it creamy; then stir everything together until completely combined to create the sauce. Add the pasta and toss to evenly coat with the sauce. For a creamier pasta (recommended), stir in desired amount of reserved pasta water 1/4 cup at a time until it reaches desired consistency (I use 1/2 cup).: When you press the feta , it will break into creamy ribbons that emulsify with the roasted juices, creating a glossy sauce that clings to the pasta . The sound is gentle, a soft stirring and gentle scraping of the dish. Add reserved pasta water slowly to achieve a silky texture, because too much will thin the sauce and too little will leave it clumpy. A frequent misstep is dumping all the water at once and losing control of the sauce consistency.
Taste and season with additional salt, pepper and/or red pepper flakes to taste (I like 1/4 tsp EACH more salt and pepper). For a less tangy pasta, stir in a couple teaspoons sugar or honey to taste (like you do in any tomatoes-based sauce).: Now is the moment to personalize the balance, since the brined feta and roasted tomatoes will have concentrated flavors. Tasting hot food can mute salt, so adjust in small increments and re-taste. If you oversalt, a quick remedy is adding a splash more reserved pasta water or a bit of unsalted dairy if acceptable. Avoid adding too much sweetener, which can flatten the tomato brightness.