Add the butter to a large frying pan and bring the heat to medium.
Once the butter is melted, add the shaved Brussels sprouts, garlic, salt, and pepper. Sauté for 8 minutes stirring frequently.
Cook the pasta according to the package directions and reserve ½ cup of the cooking water.
Add the pasta to the frying pan along with ¼ cup of the reserved pasta water, remaining butter, lemon juice, and Parmesan. Reduce heat to low and cook for 5 minutes. If the pasta is still dry, add the remaining pasta water.