Melt butter in a heavy skillet over medium-high heat until foaming. Add carrots and salt; cook and stir in hot butter until liquid evaporates and carrots begin to brown around the edges, 5 to 6 minutes.
Reduce heat to medium-low and pour in whisky carefully. Cook and stir until whisky is almost evaporated, about 2 minutes. Sprinkle in brown sugar; cook and stir until carrots are almost cooked through, about 5 minutes more.
Increase heat to medium-high and cook until glaze thickens, 15 to 30 seconds. Season with ground black pepper and cayenne pepper. Transfer carrots to a serving dish and garnish with thyme leaves.