Make the filling: Peel the apples and slice about 1/4 inch thick. Toss with the bourbon and lemon juice in a medium bowl.
Melt 2 tablespoons of the butter in a large skillet over medium-high heat. Add half of the apples and sprinkle with half of the granulated sugar. Cook, stirring, until the sugar dissolves and the mixture begins to simmer, about 2 minutes. Reduce the heat to medium and cook until the apples soften, about 7 minutes. Transfer to a bowl. Add the remaining 2 tablespoons butter to the skillet and repeat with the remaining apples and sugar. Add to the bowl and toss with the cinnamon and ginger. Let cool completely.
Roll one of the dough rounds on a lightly floured surface into a 12-inch disk (reserve the other dough round for another use). Transfer the dough to a baking sheet. Starting 2 inches from the edge, spoon the apple filling in a circle in the center of the dough. Fold and pleat the dough over the edge of the filling. Brush the crust with the beaten egg and sprinkle with the coarse sugar.
Bake until the crust is brown and the apples are tender and caramelized, about 55 minutes. Cool the galette briefly on a wire rack. Cut into wedges and serve.
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