Preheat the oven to 375°F. Butter the bottom and sides of a 9-by-13-inch baking dish. Use the Food Network 5-pc. Magnetic Measuring Spoon Set to measure and a spoon to combine the 1 tablespoon flour, 2/3 cup sugar, 4 tablespoons bourbon, 1/2 teaspoon salt and peaches in a medium bowl. Spread the mixture evenly in the bottom of the baking dish. Whisk together the remaining 2 1/4 cups flour, 1/2 cup sugar and 1 teaspoon salt with the baking powder. Melt the butter in a medium bowl in the microwave, then cool slightly. Mix in the half-and-half, egg and remaining 4 tablespoons bourbon. Stir the butter mixture into the dry mixture and whisk until smooth. Drop tablespoon-size dollops of the batter over the peaches evenly, leaving some space between. Bake until the top is golden and a toothpick inserted into the cake part comes out clean, about 50 minutes. Serve the cobbler warm with vanilla ice cream and fresh mint sprigs.