Put the peaches cut-side up in a 10-by-15-inch glass baking dish.
In a medium mixing bowl, whisk together the bourbon, lemon juice and vanilla extract. Pour the bourbon mixture over the peaches and baste each peach. Cover with plastic wrap and macerate at room temperature for 30 minutes.
Meanwhile, in a small bowl, stir together the mascarpone, heavy cream, confectioners' sugar, vanilla bean seeds and lemon zest until evenly incorporated. Cover with plastic wrap and store in the refrigerator. Remove 20 minutes prior to serving.
Heat a grill or grill pan over high heat.
Using your hands, rub the cut side of each peach with 2 teaspoons brown sugar. Sprinkle each peach with a pinch of the cinnamon and nutmeg.
Place the peaches cut-side down on the hot grill and cook until they are seared with grill marks and the sugar is caramelized, 6 to 8 minutes. Turn each peach over and cook for an additional 4 minutes. Remove from the grill.
Top each peach with a spoonful of the vanilla and lemon mascarpone.