Preheat your oven to 400°F. In a 9×13-inch ceramic baking dish, arrange the chicken breasts and block of feta cheese evenly spaced. Scatter the cherry tomatoes and whole garlic cloves around them. It’s okay if the dish feels a bit full.
Drizzle the olive oil over everything in the dish, then season with kosher salt, black pepper, and red pepper flakes if using. Use your hands to gently toss everything together so that the chicken and feta are well coated in the oil and seasoning. Be sure to wash your hands afterward for food safety.
Bake uncovered for about 35 minutes. Begin checking for doneness around the 30-minute mark; the chicken is fully cooked when it reaches an internal temperature of 165°F at its thickest point. In most cases, the full 35 minutes will be needed.
While the chicken and feta are baking, cook the pasta according to the package directions. Before draining, reserve 1/2 cup of the pasta water in case you need to loosen the sauce later.
Once baking is complete, transfer the cooked chicken breasts to a clean cutting board and let them rest for 5 to 10 minutes before slicing.
Optional step: Increase the oven temperature to broil and return the baking dish with just the tomatoes and feta to the oven for an additional 3 minutes to allow the tomatoes to blister and char slightly.
Use a fork or spoon to stir the softened feta and roasted tomatoes directly in the dish, pressing gently on the tomatoes and garlic to release their juices. Add the sliced fresh basil and mix well to combine. Next, stir in the cooked pasta, tossing everything until the sauce is evenly distributed and coats the pasta.
Top with the sliced chicken and gently toss to combine. Serve immediately, garnished with more fresh basil if desired. Leftovers can be stored in an airtight container in the refrigerator for up to 4 days.