In a food processor, combine the basil leaves, grated Parmesan cheese, pine nuts, minced garlic, and a pinch of salt and pepper. Pulse until finely chopped.
With the food processor running, gradually drizzle in the olive oil until the mixture is smooth and creamy. Adjust seasoning to taste.
Season the chicken breasts generously with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken breasts and cook for about 6-7 minutes on each side, or until they are golden brown and cooked through.
Lower the heat and pour the homemade pesto sauce over the chicken. Stir gently to coat the chicken.
Pour in the heavy cream and stir to combine. Allow the sauce to simmer for about 3-4 minutes until it thickens slightly.
Taste and adjust seasoning if necessary. Remove from heat and let rest for a few minutes before serving. Garnish with additional Parmesan cheese.