Preheat oven to 450°F (230°C). Roast whole red bell peppers on a baking sheet for 25-30 minutes until skins are blistered and charred. Place peppers in a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel skins, remove seeds, and roughly chop.
Bring a large pot of salted water to a boil. Cook penne pasta according to package instructions until al dente. Drain, reserving 1/2 cup pasta water, and set pasta aside.
Heat olive oil in a skillet over medium heat. Sauté minced garlic for about 1 minute until fragrant but not browned. Transfer garlic and roasted red peppers to a food processor or blender. Add heavy cream and blend until smooth.
Pour blended mixture back into skillet. Heat gently over medium-low, stirring often. Add grated Parmesan cheese and stir until melted and sauce thickens. Add reserved pasta water as needed to loosen sauce. Season with salt and black pepper to taste.
Add cooked penne pasta to skillet with sauce and toss to coat evenly. If using cooked chicken, stir it in to warm through. Remove from heat.
Serve pasta in bowls and garnish with fresh basil leaves and extra Parmesan cheese if desired. Enjoy immediately for best flavor and texture.
