Preheat the oven to 400 degrees. Slice the tops off of the peppers and remove the ribs and seeds. Set aside.
In a skillet over medium heat, add olive oil and chopped onion, sauteing until soft – about 5 minutes. Stir in 2 minced garlic cloves and cook for 1 minute. Season ground chicken breast with salt and pepper and add it to the skillet to brown. All chicken to cook completely – it should take about 10-12 minutes to brown. Stir occasionally.
While chicken is cooking, mix the tomato sauce with the heavy cream and remaining garlic clove and heat it over low heat. Stir in almost all of the fresh basil, reserving some for garnish.
Stir brown rice and 1/2 cup of parmesan cheese into chicken mixture, then add about 1/2 cup of tomato cream sauce in mixing to coat. Turn off heat. Divine the mixture evenly between the four peppers, stuffing them to the top. Place in a dish that allows the peppers to stand. Spoon a bit of tomato cream sauce over the tops, and pour the rest of the sauce into the bottom of the pan. Set the tops gently back on the peppers. Bake for 20 minutes, then cover with foil and bake for 30 more. Serve with more parmesan cheese and basil to garnish, with mashed potatoes on the side.