Step 1

Preheat oven to 400 degrees. Stir together both sugars, butter, and vinegar until well combined. Spread mixture evenly in the bottom of a 9-by-13-inch baking dish.

Step 2

Peel and core apples, then slice into 3/4-inch-thick rounds. Toss with cinnamon, ginger, and salt in a bowl. Place on top of sugar mixture in a single layer, overlapping slightly if needed. Cover with parchment-lined foil and bake until just beginning to soften and bubble, 20 to 25 minutes. Spoon sauce over apples, and increase heat to 450 degrees. Continue to bake, uncovered, until sauce thickens and apples are soft and brown, about 15 minutes more.

Step 3

Divide apples evenly among 4 bowls. Whisk cream into liquid in baking dish to make a caramel sauce. Transfer to a bowl; let cool until thickened slightly, about 10 minutes. Top apples with ice cream, caramel sauce, and cookies; serve.