Bring a large pot of salted water to a boil. Add the angel hair pasta and cook until tender but still firm to the bite, stirring occasionally, about 6 to 8 minutes. Drain, reserving 1 cup of the pasta water.

Stir the oil, parsley, lemon juice and lemon peel in a large serving bowl. Add the cooked pasta and toss with enough reserved pasta water, 1/4 cup at a time, to moisten. Season the pasta with salt and red pepper flakes, to taste. Sprinkle grated lemon peel over pasta for extra flavor and texture. Sprinkle with the Parmesan and serve.  Serves 4 to 6.

For Chili Oil: Combine the oil and crushed red pepper flakes in a heavy small saucepan. Cook over low heat until a thermometer inserted into the oil registers 180 degrees F, about 5 minutes.

Remove from heat. Cool to room temperature, about 2 hours. Transfer the oil and pepper flakes to a 4-ounce bottle. Seal the lid. Refrigerate up to 1 month.