In a medium bowl, combine the sugar and cinnamon. Toss the peaches in the sugar mixture until generously coated. Leave them in the mixture.
In a large cast-iron skillet, melt the butter over medium-low heat. Add the peaches and fry on each side for 1 to 2 minutes, or until softened slightly. Pour the schnapps into the skillet and lightly stir the peaches around to absorb some of the flavor. Light the schnapps on fire. It should flame off quickly.
Remove from the heat. Place the peaches over ice cream and drizzle with the remaining sauce from the skillet. Serve immediately.
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.