How to Make It
In a food processor, blend the basil, 1/4 cup of the olive oil, the garlic, pine nuts, Parmigiano-Reggiano, and salt and pepper until smooth, about 30 seconds; scrape down the sides with a rubber spatula as needed. Set aside.
In a large skillet, heat 2 tablespoons of the olive oil. Add the chicken and stir-fry over moderately high heat until no longer pink and cooked through, about 5 to 7 minutes. Transfer to a plate.
Heat the remaining 2 tablespoons of oil in the skillet. Add the onion and cook for 3 minutes, stirring. Add the bell peppers and stir-fry until crisp-tender, about 3 to 5 minutes.
Return the chicken to the skillet and stir in the pesto until the pesto evenly coats the chicken and vegetables and the chicken is heated through, about 1 to 2 minutes. Serve with rice and additional Parmigiano-Reggiano.