In a food processor, combine flour, brown sugar, white sugar, cinnamon and cold butter. Pulse until a coarse mixture is formed, and no pieces are larger than a pea, about 12 1-second pulses. Add oats and toss to combine, pressing pieces together with fingertips. Cover with plastic wrap and refrigerate.
In a Dutch oven, combine cranberries with 3/4 c sugar, water, and, if using, crystallized ginger and wine. Cook over medium heat about 10 minutes, until cranberries break down and the sauce becomes jammy (20 minutes if cranberries are still frozen). Transfer cranberries to a bowl and set aside.
Add the apples to the same hot Dutch oven. Add remaining 1/2 c sugar and dried cranberries. Stir over medium heat 5 minutes, until apples release their juices. Add tapioca and cooked cranberries to Dutch oven and stir well to combine. Pour mixture into 9×13“ baking dish and spread out evenly. Place dish on a large rimmed baking sheet to catch any bubble-overs.
Sprinkle topping evenly over the top of the fruit mixture. Bake in a preheated 400°F oven for 30 minutes, until the juices bubble at the edges and the topping is browned. Allow to cool 30 minutes before serving. Serve with vanilla ice cream.