Preheat the oven to 400°F.
Place the block of feta cheese in the center of a baking dish.
Scatter cherry tomatoes and drained chickpeas around the feta.
Drizzle olive oil over the feta, tomatoes, and chickpeas. Add minced garlic, dried oregano, salt, pepper, and red pepper flakes if using. Toss gently to coat.
Bake for 20 to 25 minutes until tomatoes burst and feta is golden and soft.
While baking, bring a pot of salted water to a boil and cook pasta until al dente according to package directions. Drain, reserving some pasta water.
Remove the baking dish from the oven and mash the softened feta and tomatoes with a fork to create a creamy sauce.
Add cooked pasta to the baking dish and toss to combine. Add reserved pasta water if the sauce needs loosening.
Serve divided into bowls and garnish with fresh basil or parsley. Optionally add extra olive oil or cracked black pepper.