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Preheat the oven to 350°F (325°F if using a convection oven).
Peel, core, and cut 1 pound Granny Smith apples into 3/4-inch pieces. In a large bowl, combine the apples, 1 1/2 cups fresh or frozen blackberries, 1/4 cup granulated sugar, and 1 tablespoon water; stir gently to combine.
Optionally, cook the fruit mixture in a saucepan over medium heat for 5 to 7 minutes, until the apples just begin to soften. Then spoon the fruit into an 8-inch baking dish (or layer it directly if you skipped cooking).
In a separate bowl, combine 1 2/3 cups all-purpose flour and 1/4 cup granulated sugar. Add 1 stick of cold, cubed unsalted butter and use your fingertips or a pastry blender to work it into the flour mixture until it resembles coarse crumbs.
Stir in 1/2 cup rolled oats and 2 tablespoons demerara sugar, then evenly sprinkle the topping over the fruit without pressing it down.
Bake for 30 to 40 minutes, until the topping is golden brown and the filling bubbles around the edges. If it browns too quickly, loosely cover the dish with foil.
Let the crisp rest for a few minutes before serving warm. Serve with custard, vanilla ice cream, or whipped cream, if desired.