Roast the garlic. Roast the garlic until soft and golden according to your preferred oven-roasting method. Once cool enough to handle, squeeze the softened cloves from their skins and mash them. For a quicker option, use about 6 cloves of minced garlic and sauté them with the onion.
Roast the peppers. Set the oven to broil. Arrange the red bell pepper quarters skin-side up on a foil-lined baking sheet. Broil for about 10–15 minutes, or until the skins are heavily blackened.
Steam and peel the peppers. Carefully transfer the hot peppers to a sealed heat-safe container or bag and let them steam for about 10 minutes. Remove the loosened skins with your fingers, then roughly chop the roasted peppers.
Cook the pasta. Bring a large pot of generously salted water to a boil. Cook the fettuccine according to the package directions until al dente. Drain and set aside.
Cook the onion. While the pasta cooks, heat the olive oil in a large pot over medium heat. Add the diced onion and cook for about 5 minutes, until softened. If using minced raw garlic instead of roasted garlic, add it during the final minute.
Blend the vegetables. Carefully transfer the roasted peppers, roasted garlic, and softened onion to a blender or food processor. Blend until smooth and creamy.
Make the sauce. Melt the butter in the same pot over medium heat. Pour in the roasted pepper mixture. Add the broth, heavy cream, and milk. Season with salt and black pepper, then stir well and gently heat until the sauce is warmed through.
Add the cheese. Remove the pot from the heat. Stir in the freshly grated Parmesan and chopped parsley until the cheese melts into the sauce.
Combine with pasta. Add half of the cooked fettuccine and gently toss until coated. Add the remaining pasta and toss again until evenly covered with the sauce.
Serve. Garnish with additional Parmesan and fresh parsley. Serve the Roasted Garlic and Red Pepper Fettuccine Alfredo immediately while warm and creamy.