Marinade: In a mixing bowl, mix together 1 cup olive oil, 1/4 cup parsley, lemon juice, 2 tbsp hot sauce, 3 cloves garlic, 1 tbsp tomato paste, 2 tsp oregano, 1 tsp salt, and 1 tsp black pepper. Reserve a small amount for basting later. Pour remaining marinade into a large resealable plastic bag with shrimp. Seal, and marinate in the refrigerator for 2 hours.
Sautee red and green pepper.
Skewer and grill shrimp, whiles basting with marinade.
Meanwhile, pour 2 cups cream into large skillet. Cook over medium heat, stirring constantly, until just about boiling. Reduce heat, and add 1 tbsp basil, 1tbsp thyme, 2 tsp salt, 2 tsp black pepper, 1.5 tsp crushed red pepper flakes, 1 tsp white pepper, 1 cup chopped green onions, 1 cup chopper parsley, and sauteed peppers. Simmer 7 to 8 minutes, or until thickened. Add cheese until melted.
Pour sauce over pasta, and top with grilled shrimp.