Heat 6 quarts water to boil and add 2 tablespoons salt.
In a 12- to 14-inch saute pan, heat olive oil, red pepper and garlic over low heat until just fragrant, about 2 minutes, and remove from heat. Cook spaghetti according to package instructions until just al dente. Drain and pour into oil mixture and add parsley. Toss to mix well over medium heat and pour into warmed serving bowl. Shave Bottarga over bowl, sprinkle with lemon zest and serve immediately.