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