Heat 1½ Tbsp. of the oil in a large skillet over medium heat. Add shallots; cook 3 minutes. Add pear, maple syrup, and ¼ tsp of the salt; cook 3 minutes. Stir in balsamic and cook 8 to 10 minutes, until pears are softened and mixture is golden. Stir in rosemary and transfer to a bowl.Add remaining 1½ Tbsp. oil to pan. Arrange Brussels, cut side-down, and cook, undisturbed, for 4 minutes, until golden-brown. Toss and continue to cook, stirring occasionally, until Brussels are crisp-tender, about 5 more minutes. Season with remaining ½ tsp. salt.Transfer sprouts to a serving platter or bowl and top with chutney.