Preheat the oven to 350 degrees. On a work surface,
stack the phyllo sheets and cut out four 7-inch squares (12 total), discarding the scraps. Stack the squares between 2 sheets of wax paper and cover with a kitchen towel.
Spray the countertop and 4 individual ring molds with nonstick cooking spray. Lay a square of phyllo on the counter and sprinkle with some of the 2 teaspoons of sugar; lay a second square on top, brush with the melted butter, and sprinkle with sugar. Cover with a third layer and sprinkle with sugar.
Work the phyllo into the ring mold as you would a handkerchief into a pocket, letting the edges overhang. Repeat with the remaining phyllo. Place the molds on a parchment-lined baking sheet and bake for 10 to 12 minutes, or until golden brown. Carefully transfer the phyllo shells to a rack.
Combine the apples, lemon juice, and apple juice and set aside. In a nonstick skillet, melt the butter over medium heat. Add 1 tablespoon sugar and caramelize for 3 minutes, or until golden brown. Remove from the heat, add the Cognac, and stir with a wooden spoon. Return the pan to the heat, add the spices and apple mixture, and cook, stirring occasionally, until the apples are tender, about 5 minutes.
Divide the apples among the shells and sprinkle with crystallized ginger.