Bring a large pot of water to a boil. Cook pasta according to package directions.
Melt 1 1/2 tablespoons butter in a medium saucepan over medium heat. Stir in flour and cook until smooth. Slowly stir in milk and cream; simmer, stirring constantly, until thickened. Stir in lemon thyme, parsley, garlic, Parmesan cheese, salt, pepper, Worcestershire sauce and hot sauce. Reduce heat to low and allow to simmer
Meanwhile, steam broccoli until done.
Melt 1 tablespoon butter in a large skillet. Saute shrimp and garlic until done.