Set your oven to 400°F so it is fully hot when the pan goes in. A properly preheated oven helps the sprouts roast fast and brown well. I always do this first so nothing waits on the oven later.
Cut off the dry bottom of each sprout and remove any loose or yellow outer leaves. Slice each sprout in half from top to bottom. Halving gives you a flat cut side, which is the secret to great browning.
Place your cast-iron skillet over medium-high heat and pour in the olive oil. Wait until the oil shimmers and looks loose and glossy. Don't rush this step, because hot oil is what starts the sizzle.
Lay the sprouts cut side down in one single layer. Tuck the peeled garlic cloves between them, then sprinkle with salt and pepper. Make sure the sprouts fit without crowding, or they will steam instead of brown.
Leave the sprouts alone and let the bottoms cook until they start to brown. Resist the urge to stir. This still, hands-off time builds the caramelized flavor that makes these sprouts special.
Carefully move the skillet into the oven. Roast for about 10 to 20 minutes, shaking the pan every 5 minutes. They are done when they look deeply browned and feel tender when poked with a fork.
Taste a sprout and adjust the salt and pepper if needed. Stir in the balsamic vinegar, using it sparingly so it doesn't overpower the dish. The vinegar sizzles and coats the sprouts in a light, tangy glaze.
Transfer the sprouts to a serving dish while they are still hot. They taste great warm too, which is handy on a busy holiday table. Serve right away for the best crunch