Heat the oven to 425F with a large rimmed sheet pan inside so it gets hot.

Trim the stem ends of the sprouts, pull off any loose yellow leaves, and cut each one in half from top to bottom. Pat them dry with a towel.

Toss the sprouts in a bowl with the olive oil, salt, and pepper until coated. Carefully pull the hot pan from the oven and spread the sprouts on it in a single layer, cut side down. Do not crowd them; use two pans if needed.

Roast 20 to 25 minutes without stirring, until the cut sides are deep brown and the outer leaves are crisp and charred at the edges.

While they roast, put the balsamic vinegar, maple syrup, Dijon, and minced garlic in a small skillet over medium heat. Simmer 2 to 3 minutes, until it thickens enough to coat a spoon. Pull it off the heat; it will thicken more as it cools.

Transfer the roasted sprouts to a serving bowl, pour the glaze over, and toss to coat. Taste and add a pinch of salt if needed. Serve right away while the edges are still crisp.