Heat butter over medium heat in a large, deep skillet. Once melted, add the garlic and saute 1 minute. Add the halved tomatoes, crushed red pepper, salt, and brown sugar; cook 3-4 minutes stirring often.
Pour in the chicken broth and add linguine (uncooked), increase heat to high. Bring to a boil, reduce heat to medium and simmer 10 minutes. Add half and half and simmer an additional 2-3 minutes or until pasta is al dente.
Add parsley and shrimp. Cook 2-3 minutes or until shrimp are cooked through. Add grated Parmesan and mix well; simmer an additional 1-2 minutes. Serve hot.