3 tablespoons (¾ stick) Butter
½ pound Shallots, thinly sliced
Coarse Kosher Salt
2 tablespoons Apple Cider Vinegar
4 teaspoons Sugar
3 tablespoons (¾ stick) Butter
1 ½ pounds Brussels Sprouts, trimmed and halved through the stem
3 tablespoons Olive Oil
Salt and Black Pepper
Arrange an oven rack to the lower middle position, preheat the oven to 450 degrees F.
Line a rimmed baking sheet with parchment paper and toss together on the sheet: brussels sprouts, 3 tablespoons olive oil, and season generously with salt and black pepper.
Arrange brussels sprouts in a single layer, cut sides down. Roast until golden brown and crisp, 20 to 25 minutes.
Melt 3 tablespoons butter in medium skillet over medium heat. Add shallots; sprinkle with coarse kosher salt and pepper. Sauté until soft and golden, about 10 minutes. Add vinegar and sugar. Stir until brown and glazed, about 3 minutes.