Arrange a rack in the middle of the oven and heat the oven to 400ºF.

Cut 1 pound broccoli crowns into 1 ½- to 2-inch-wide florets (about 6 ½ cups) and place in a 9x13-inch baking dish. Peel and smash 3 garlic cloves and add to the baking dish. Add ½ cup of the olive oil, ¼ teaspoon kosher salt, and ¼ teaspoon red pepper flakes if using. Stir to coat.

Push the broccoli to the edges of the baking dish. Place 1 (8-ounce) block feta cheese in the center. Drizzle the feta with the remaining 1 tablespoon olive oil.

Bake until the feta is golden-brown in spots, and the broccoli is crisp-tender and lightly browned at the edges, 25 to 30 minutes. Meanwhile, cook the pasta and prepare the lemon and basil.

Bring a large pot of salted water to a boil. Add 12 ounces dried bowtie pasta and cook according to the package instructions until al dente. When the pasta is ready, reserve 1 cup of the pasta water. Drain the pasta.

Juice ½ medium lemon until you have 1 tablespoon. Pick the leaves from ½ small bunch fresh basil and coarsely chop until you have ¼ cup.

When the broccoli and feta are ready, remove from the oven. Add ¾ cup of the reserved pasta water and stir to combine. Add the drained pasta and lemon juice, and stir to combine. Let sit for 5 minutes for the sauce to thicken slightly. For a thinner sauce, stir in more pasta water 1 tablespoon at a time. Add the basil and stir to combine. Taste and season with more kosher salt as needed.