Melt butter in a skillet; add apple and brown sugar, and saute until tender. Stir in brandy; cook just until heated (do not boil). Remove from heat, and ignite with a long match; let flame 1 minute. Keep warm.
Grate potatoes and onion; combine vegetables, egg, and next 3 ingredients.
Drop mixture by tablespoonfuls into hot oil in a large skillet over medium-high heat; fry 5 minutes or until crisp, turning once. Drain on paper towels, and place in a shallow baking dish. Cut goat cheese into 1/4-inch-thick slices, and place slices over pancakes.
Bake at 350° for 5 minutes. Serve pancakes with apple mixture.
Note: You may substitute apple juice for applejack brandy and omit flaming step.