Preheat the oven to 400 degrees. In a large baking dish, toss together the tomatoes, garlic, shallot olive oil, red pepper flakes, if using, and oregano. Nestle the block of feta cheese in the center and place in the oven. Bake for 35-40 minutes, until tomatoes are bursting and bubbly.
While the feta and tomatoes bake, bring a large pot of salted water to a rolling boil. Cook the pasta to al dente. Reserve 1 cup of pasta water and drain the pasta.
Add the hot pasta to the dish of hot tomatoes and stir well to combine. Add some of the reserved pasta water as needed, just a couple of tablespoons at a time. The feta will melt into the tomato juices to create a creamy sauce that soaks into the pasta. Season with salt and pepper, and any desired optional garnishes, and eat right away while it’s hot.