Stir together brown sugar, salt, and cinnamon in a small bowl, and set aside.

Melt butter in a large cast-iron or nonstick skillet over medium. Add half of the apple slices in a single layer. (Don’t overcrowd the pan.) Cook, turning once, until slightly softened but still quite firm, 2 to 3 minutes per side. Transfer to a plate using a slotted spoon. Repeat process with remaining apples.

Return cooked apple slices to hot skillet, and add cider and reserved brown sugar mixture. Cook over medium, gently turning occasionally, until apples are glazed, browned, and tender, 3 to 4 minutes. Transfer fried apples to a serving bowl or plate. Serve warm.