Set a pot of salted water to boil. Cook pasta according to package directions until just al dente. Drain, reserving 1 cup of pasta water.
While pasta is cooking, heat olive oil in a large sauté pan or skillet. Add garlic and crushed red pepper. Cook, stirring frequently, for about 2 minutes. Reduce heat if garlic starts to brown. Turn off heat and stir in lemon zest.
When pasta is done, add to skillet along with lemon juice and a little pasta water, and return to medium flame. Add parsley. Toss to combine everything, adding more water as needed to moisten pasta, if dry. Cook until heated through, 1 or 2 minutes.
Add 1/2 cup grated Parmesan and toss to combine. Taste and season with salt and pepper, as needed.
Divide among 4 shallow pasta bowls and top with additional grated Parmesan, to taste. Serve.