Bring a large pot of salted water to boil. Cook the pasta until al dente, then drain, reserving ¼ cup of cooking water.
Meanwhile, in a large nonstick skillet, heat the oil over a medium-high flame. Cook the garlic until beginning to brown, about 2 to 3 minutes. Add the shallot and the asparagus and lower the heat to medium. Saute the asparagus until it turns a vibrant green and is slightly tender, about 3 minutes. Season with ½ teaspoon salt and the red pepper flakes.
Add the cream, lemon juice, and zest. Gently simmer until partially reduced, about 3 minutes. Remove the pan from the heat and add the peas, stirring to coat.
Add the cooked pasta to the sauce, along with the arugula, and gently toss until everything is combined and the arugula is wilted. Serve immediately.