Preheat the broiler. Halve and pit the peaches, then lightly score the cut sides of each peach a few times with a knife.
Combine the liqueur and butter in a medium ovenproof skillet over medium heat; cook, stirring, until the butter melts and the liquid just begins to simmer. Add the peaches, cut-side up, and cook until the bottoms begin to soften, about 4 minutes. Sprinkle each peach half with 1 teaspoon sugar and transfer the skillet to the broiler. Broil until the peaches brown in spots, about 3 minutes. Let cool slightly.
Divide the peaches among plates and drizzle with the syrup from the skillet. Serve with the mascarpone.