How to Make It
In a large pot of boiling salted water, cook the spaghetti until it is al dente. Drain the spaghetti well, reserving 1/2 cup of the pasta cooking water.
Meanwhile, in a large skillet, heat the olive oil. Add the garlic and crushed red pepper and cook over moderate heat until the garlic is tender, about 3 minutes. Add the tomatoes, season with salt and pepper and cook over moderately high heat until the tomatoes begin to release their juices, about 2 minutes. Add the spinach and cook until wilted, about 2 minutes.
Add the spaghetti, the reserved 1/2 cup of pasta cooking water and the 1/4 cup of pecorino to the skillet and toss over low heat until the pasta is coated with the sauce. Season with salt and pepper. Add the goat cheese and toss gently. Transfer the spaghetti to shallow bowls and serve, passing additional grated pecorino cheese at the table.