Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions until al dente, usually about 10-12 minutes. Once cooked, reserve ½ cup of pasta water, then drain the rest and set the pasta aside.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the sliced chicken breast, seasoning with salt and pepper. Sauté the chicken until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, reduce heat to medium and add the minced garlic. Sauté briefly until fragrant, about 30 seconds. Pour in the 2 cups of heavy cream, stirring constantly. Let the cream simmer gently for 3-4 minutes to thicken slightly.
Stir in the grated Parmesan cheese until fully melted and the sauce is smooth. Add the roasted red pepper slices, folding them gently into the sauce. If the sauce seems too thick, add a little reserved pasta water to reach your desired consistency.
Return the cooked chicken to the skillet and toss everything together with the drained fettuccine pasta. Stir well to coat the pasta evenly with the Alfredo sauce and distribute the chicken and peppers.
Sprinkle chopped fresh parsley over the top for a burst of color and fresh flavor. Serve immediately while warm and enjoy the creamy, savory goodness of your homemade Chicken Alfredo with Roasted Red Peppers.