Drain the jar of roasted red peppers and roughly chop the peppers; peel and slice the garlic cloves.
Heat 3 tablespoons extra virgin olive oil in a skillet over medium heat, add the garlic and chopped roasted peppers, and cook, stirring, for 2–3 minutes until fragrant.
Transfer the pepper and garlic mixture to a blender, cover the lid with a tea towel to prevent splatter, and puree until smooth.
Add 1 cup heavy cream to the blender and puree again until you have a thick, creamy sauce; set aside.
Place the chicken breasts on a cutting board, cover with baking paper or clingfilm, and pound with a meat mallet or rolling pin to about 1/2-inch thickness.
Season both sides of the flattened chicken with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Heat 1 tablespoon olive oil in a heavy-based skillet over high heat. When hot, cook the chicken 2–3 minutes per side until just cooked through, then remove and tent with foil to keep warm.
While the chicken cooks, bring a large pot of water to a boil. Add 1 tablespoon salt and the pasta, then cook the pasta for 2 minutes less than the package directions for al dente.
Reserve 2 cups of the pasta cooking water, then drain the pasta in a colander and return the pasta to the pot.
Add the roasted red pepper cream sauce and 1/2 cup of the reserved pasta water to the pasta. Stir and bring to a gentle simmer, adding more pasta water as needed to reach a silky sauce that coats the pasta; simmer until pasta is al dente.
Slice the cooked chicken and serve it over or alongside the red pepper pasta.