Apple Ginger Honey Cake

Ingredients路  For the Syrup:路 1 cup sugar (7 ounces; 200g)路 1 1/2 cups unsweetened apple juice (12 ounces; 340g)路 2-inch piece ginger (2 ounces; 60g), unpeeled, cut in half lengthwise and smashed路 Zest from 1 medium lemon路 1 tablespoon fresh lemon juice (1/2 ounce; 14g), from about 1 lemon路 4 tablespoons Applejack brandy (2 ounces; 60g) Black DirtDistillery is kosher路