Cook pasta according to directions. Meanwhile, melt butter in medium saucepan over medium heat. Stir in the flour and cook for 1 minute. Using a whisk, slowly add milk and half and half, whisking to help prevent lumps from forming. Add the red pepper and garlic and simmer for 10 minutes on low. Pour mixture into a blender and puree until smooth. Return to pan and stir in parmesan cheese. Add salt and pepper to taste and stir in chicken, broccoli and mushrooms. Simmer until pasta is done cooking, drain pasta and add to sauce.