Roast the peppers: Set the oven to broil. Place the red bell pepper quarters skin-side up on a foil-lined baking sheet. Broil for 10–15 minutes, or until the skins are heavily blackened and blistered.
Steam the peppers: Carefully transfer the hot peppers to a sealed food-safe bag or covered heatproof container. Let them sit for about 10 minutes. Remove the skins with your fingers, then roughly chop the softened peppers.
Cook the fettuccine: 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: Meanwhile, heat olive oil in a large 5-quart pot over medium heat. Add the diced onion and cook for about 5 minutes, until soft and translucent.
Blend the vegetables: Add the roasted peppers, roasted garlic, and cooked onion to a blender or food processor. Blend until smooth and creamy.
Build the sauce: Melt the butter in the same pot over medium heat. Pour in the roasted pepper and garlic puree. Add the broth, heavy cream, and milk. Season with salt and black pepper, then stir well.
Simmer gently: Allow the sauce to warm through for a few minutes, stirring occasionally. Avoid boiling vigorously, as the dairy can become less smooth.
Finish the Alfredo sauce: Remove the pot from the heat and stir in the freshly grated Parmesan and chopped parsley.
Toss the pasta: Add half of the cooked pasta and gently toss until coated. Add the remaining fettuccine and continue tossing until all the noodles are covered with the sauce.
Serve: Spoon the pasta into bowls and garnish with additional grated Parmesan and fresh parsley. Serve immediately.