In a large pot of boiling salted water, cook pasta according to package instructions. Reserve 1 cup pasta water; drain pasta and return to pot. Meanwhile, in a small pot, heat oil over medium. Add shallots, season with salt and pepper, and cook, stirring, until tender, 4 minutes. Add cream and lemon zest. Bring to a boil and cook until slightly thickened, 8 minutes. Add lemon juice and season to taste with salt and pepper. Pour cream sauce over pasta and toss, adding enough pasta water to create a thin sauce that coats pasta.