Lay out a piece of plastic wrap and place 1-2 chicken breasts on it. Place another piece of plastic wrap over the top. Use a meat mallet or rolling pin to pound the chicken to an even thickness. Repeat with the other chicken breasts.
In a shallow bowl, whisk together the flour, salt, pepper, and garlic powder. Dip chicken in the flour until coated all over.
Add a large drizzle of olive oil to a large skillet and place over medium heat. Once hot, add the chicken and cook for 5-8 minutes per side until cooked through and lightly browned. Transfer the chicken to a plate, cover with foil, and set aside.
To the same skillet, add the pesto and cook for 1-2 minutes over medium heat until fragrant. Add the heavy cream and stir until warmed through and starting to bubble. Season with salt and pepper to taste.
Add chicken and any juices on the plate back to the pan, sprinkle parmesan cheese on the chicken, and cook until cheese is melted. Sprinkle with freshly chopped basil or parsley for garnish before serving warm.