Step 1

Heat the pancetta and 1 tablespoon of the oil in a heavy 10-inch straight-sided saute pan over medium-low heat until golden and crisp all over, 10 to 15 minutes. With a slotted spoon, transfer the pancetta to a plate lined with paper towels, leaving the drippings in the pan.

Step 2

You should have about 2 tablespoons of drippings left in the pan; if not, add the remaining tablespoon of oil. Measure out 1/2 cup water and set aside. Put the pan over medium-high heat and arrange the sprouts cut-side down in a single layer. Cook until nicely browned, 2 to 3 minutes. Add the water to the pan, cover immediately and simmer until the sprouts are tender when poked with a fork or skewer, about 3 minutes. (If the water evaporates before the sprouts become tender, add more water 1/4 cup at a time.) Transfer the sprouts to a plate with a slotted spoon.

Step 3

Return the pan to medium-high heat. (It is fine if any water remains; it will boil off with the vinegar.) Add the vinegar and a few grinds of pepper and boil the vinegar until lightly syrupy and reduced to about 2 tablespoons, about 2 minutes. Reduce the heat to low, add the butter and stir until melted. Return the sprouts and pancetta to the pan and toss to evenly coat with the sauce. Season with salt and more pepper.