In a heavy 10 inch saute pan, set over medium low heat, slowly cook pancetta in 1 tablespoons olive oil until golden and crisp all over. About 15 minutes. With slotted spoon, transfer pancetta to a plate lined with a paper towel, leaving fat in pan. You should have about 2 Tbsps. of fat remaining, if not add remaining 1 tablespoons oil to pan. Have ready 1/2 cup water.
Put the pan over medium high heat and arrange the sprouts cut side down in a single layer. Cook undisturbed until nicely browned, 2 to 3 minutes. When the sprouts are browned, add water to the pan, cover immediately and simmer until the sprouts are tender. If water evaporates before sroupts are tender, add more water, 1/4 cup at a time. With a slotted spoon, transfer sprouts to a bowl. Return pan to medium high heat, and if any water remains, let it boil off.
Add balsamic vinegar and a few grinds of pepper. Boil vinegar until it's reduced to about 2 Tbsps., and looks syrupy. About 2 minutes. Reduce heat to low, and add butter, and stir until it's melted. Return sprouts and pancetta to the pan and swirl and shake the pan until the sprouts are evenly coated. Season with salt and more pepper, and serve.