Drain the jarred roasted peppers and roughly chop them. 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 and puree until smooth.
Add 1 cup heavy cream to the blender and puree again until you have a thick, silky sauce; set aside.
Place the chicken breasts between baking paper or clingfilm on a cutting board and pound with a meat mallet or heavy rolling pin until about 1/2 inch (1.3 cm) thick.
Season both sides of the flattened chicken with 1/2 teaspoon salt and 1/4 teaspoon black 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. 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 long pasta, and cook for 2 minutes less than the package directions.
Reserve 2 cups of pasta cooking water, then drain the pasta in a colander and return the pasta to the pot.
Add the roasted red pepper sauce and 1/2 cup of the reserved pasta water to the pasta. Bring to a gentle simmer and cook until the pasta is al dente, adding more reserved water if the sauce becomes too thick.
Slice the cooked chicken and serve it arranged over the sauced pasta.