Peel the peppers and seed them. Cut away any white pith inside the peppers and cut into ¾-inch squares.
Lightly crush and peel the garlic cloves and put them in a heavy-bottomed braising pan with the olive oil. Place over medium-high heat and sauté until the garlic is lightly browned on all sides, 1 to 2 minutes. Remove the garlic and discard. Add the peppers to the oil and season with salt. Sauté until the peppers are tender and lightly browned, 10 to 15 minutes.
While the peppers are sautéing, put the broth in a pot over high heat and bring to a boil. Lower the heat to maintain a very gentle simmer.
When the peppers are done, add the rice and stir until it is well coated. Add about 1cup of the hot broth and continue stirring. Add only enough broth to produce the consistency of a rather thick soup and wait until all the liquid is absorbed before adding more. Season with salt. When the rice has cooked about 10 minutes, tear the basil leaves into fairly wide strips and add them to the risotto. Continue adding broth and stirring until the rice is al dente, 20 to 25 minutes.
Remove the risotto from the heat and stir in the butter and Parmigiano. Serve at once.