Stem, seed and remove ribs from peppers. Cut lengthwise into 1-inch-wide strips; leave curved ends intact. Cut onion in half lengthwise, and slice into 1/4-inch-thick semicirclesAdvertisement
Heat oil and butter in a large skillet over medium heat. Add garlic and onions, and cook for about 2 minutes. Add pepper strips and sugar, and toss for 2 to 3 minutes. Cover pan, and turn heat to low. Cook, stirring occasionally, until peppers are very soft, 30 to 35 minutes.
Remove cover; raise heat to medium. Cook stirring often, until most of the liquid evaporates and peppers are nicely glazed, about 3 minutes. Add a little water, if necessary, to avoid scorching. Season with salt and pepper. Serve peperonata warm or at room temperature.