Step 1: Preheat your oven to 375°F (190°C). Lightly grease an 8x8 inch baking dish or a similar oven-safe dish.
Step 2: In a large bowl, combine the pitted and sliced plums, 1/2 cup granulated sugar, cornstarch, lemon juice, and ground cinnamon. Toss gently to coat the plums evenly. Pour the plum mixture into the prepared baking dish, spreading it out evenly.
Step 3: In a separate medium bowl, combine the rolled oats, all-purpose flour, brown sugar, 1/4 cup granulated sugar, and salt. Whisk these dry ingredients together until well combined.
Step 4: Add the cold, cubed unsalted butter to the dry ingredients. Using your fingertips, a pastry blender, or a fork, work the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining. Avoid overmixing.
Step 5: Sprinkle the crumble topping evenly over the plum filling in the baking dish. Do not press it down too firmly.
Step 6: Place the baking dish on a baking sheet (to catch any potential overflow) and bake for 35-45 minutes, or until the topping is golden brown and the fruit filling is bubbling thickly. The juices should be visibly escaping from the sides.
Step 7: Remove from the oven and let it cool for at least 15-20 minutes before serving. This allows the fruit filling to set slightly and intensifies the flavors. Serve warm with your favorite accompaniments.