Preheat the oven to 400°F (200°C) and place a rack in the middle.
Arrange tomatoes on a rimmed baking sheet, drizzle with 2 tablespoons of olive oil, sprinkle with salt, and toss to coat.
Place the feta block in the center of the baking dish surrounded by tomatoes and place garlic cloves in between tomatoes.
Drizzle with the remaining two tablespoons of olive oil, and sprinkle with oregano, red pepper flakes, and pepper.
Bake for 40 minutes or until the tomatoes have burst their skins.
In the meantime, bring a large pot of salted water to a boil. Cook the pasta al dente according to package instructions. Reserve one cup of pasta water and then drain the pasta.
Remove from the oven to allow it to cool slightly.
Transfer tomatoes and feta into a large bowl with all the juices and the garlic and mash with a fork or blitz until evenly combined.
Mix the sauce with the pasta, adding the reserved pasta water until reaching the desired creamy consistency. Take a taste and adjust the seasoning as needed.
DONE!