01 - Preheat oven to 350°F. Lightly grease a baking dish large enough to hold persimmon halves in a single layer.
02 - Place persimmon halves cut side up in the prepared baking dish.
03 - In a small bowl, combine 2 tablespoons brown sugar, cinnamon, ginger, nutmeg, and lemon juice. Mix thoroughly until well blended.
04 - Spoon the spiced sugar mixture evenly over each persimmon half.
05 - In a medium bowl, combine oats, flour, 1/4 cup brown sugar, salt, and nuts if using. Add cold butter and rub with fingertips until mixture resembles coarse crumbs.
06 - Sprinkle oat crumble generously over the filled persimmons.
07 - Bake for 30 to 35 minutes until topping is golden brown and persimmons are tender and bubbling.
08 - Allow to cool slightly before serving. Serve warm, optionally topped with vanilla ice cream or Greek yogurt.