Prepare a bowl of ice water and set aside. Bring a large pot of salted water to a boil. Add the green beans and cook until bright green and just barely cooked through, 2 to 3 minutes. Use a spider or strainer to transfer the green beans to the ice bath and let cool completely before draining. Add the bucatini to the same pot of boiling water. Let cook to al dente, about 3 minutes less than the package instructions.
Meanwhile, heat the olive oil in a large saute pan over medium-high heat. Cook the garlic and red pepper flakes until fragrant but not browned, about 1 minute, then add the lemon zest and juice and approximately 1/4 cup pasta water.
Use tongs to transfer the pasta directly to the saute pan. Add the butter and blanched green beans, then toss to coat the pasta and beans in the sauce. Keep cooking, tossing, until the pasta is al dente and the sauce is glossy and thickened, about 3 minutes more. Turn off the heat and gradually stir in the Pecorino, tossing constantly. Season with salt and freshly ground black pepper.
Divide pasta among 4 serving bowls and garnish with the parsley, more Pecorino and a drizzle of olive oil.