Preheat oven to 400°F (200°C). In a 9x13-inch baking dish, place the block of feta in the center. Scatter the cherry tomatoes and minced garlic around the feta.
Drizzle the olive oil generously over everything. Sprinkle with red pepper flakes (if using), salt, and black pepper. Gently toss the tomatoes to coat, but leave the feta intact.
Bake for 30–35 minutes, until tomatoes have burst and softened, and the feta is golden and soft.
Meanwhile, bring a large pot of salted water to a boil. Cook pasta until al dente according to package directions. Reserve 1 cup of pasta water, then drain.
Remove the baking dish from the oven. Immediately add the drained pasta and a splash of pasta water. Use tongs or a wooden spoon to toss everything, mashing the feta and tomatoes into a creamy sauce. Add more pasta water as needed to reach your desired consistency.
Taste and adjust salt and pepper. Divide into bowls, top with torn fresh basil, a drizzle of olive oil, and extra red pepper flakes if you like heat.