Preheat the oven to 400°F (200°C). Place the cherry tomatoes on a baking sheet, drizzle with olive oil, and season with salt and pepper. Roast in the preheated oven for about 15 minutes until the tomatoes are slightly charred and softened.
While the tomatoes are roasting, cook the Casarecce pasta according to the package instructions until al dente. Drain and set aside.
Season the chicken breasts with salt and pepper. Heat 1 tablespoon of olive oil in a skillet over medium heat. Cook the chicken breasts for about 6-8 minutes per side until they are cooked through and no longer pink in the center. Remove from the skillet and let them rest for a few minutes. Slice the chicken into thin strips.
In the same skillet, reduce the heat to low and add the heavy cream. Stir in the pesto sauce and grated Parmesan cheese. Cook for a few minutes until the sauce thickens and the cheese is melted, stirring constantly.
Add the cooked Casarecce pasta to the skillet with the pesto cream sauce. Toss gently to coat the pasta evenly.
Serve the pasta in individual bowls or plates. Top with the sliced chicken and roasted cherry tomatoes. Garnish with fresh basil leaves.