Heat the oil in a large, heavy-bottomed skillet over medium-high heat.
Add the sprouts to the skillet, arranging them in a single layer, cut side down. Cook for 3 to 5 minutes without moving the sprouts, until the cut sides are nicely browned.
Turn the sprouts over, add the smashed garlic, and season with salt and pepper. Cook for 3 to 5 minutes more, until the sprouts are tender.
Remove the skillet from the heat and immediately pour the balsamic vinegar over the sprouts. Stir to mix and serve immediately.