Step 1

Preheat the oven to 400 degrees F (200 degrees C).

Step 2

Combine grape tomatoes, asparagus, zucchini, onion, bell pepper, and corn kernels in a baking dish large enough to accommodate all vegetables. Drizzle generously with olive oil and sprinkle with pepper flakes as well as a hit of salt and pepper. Toss to coat and make a well in the center of the dish. Place feta blocks in the well and drizzle with more olive oil. Season feta with salt, pepper, and a pinch of pepper flakes. Nestle thyme sprigs into the veggies around the dish.

Step 3

Bake uncovered in the preheated oven until vegetables are soft and feta is lightly browned, about 40 minutes.

Step 4

When the vegetables and feta have cooked for 25 minutes, bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until tender yet firm to the bite, about 12 minutes. Drain, reserving 1 cup of pasta water. Set aside.

Step 5

When the vegetables and feta are finished cooking, turn the broiler to 500 degrees F (260 degrees C) and broil vegetables for 1 minute for some final browning.

Step 6

Squeeze lemon over vegetables and feta and stir in fresh parsley. Stir in rigatoni and reserved pasta water to help feta coat pasta evenly. Season with salt and pepper as needed and sprinkle with Pecorino Romano cheese.