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 9x13" 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.