Preheat oven to 350 degrees.
Grease a 9x13 baking dish.
Place chopped plums in the baking dish and toss with granulated sugar, 1/2 cup brown sugar, and cornstarch until coated.
In a medium bowl, whisk together the rolled oats, flour, 1/4 cup brown sugar, cinnamon, nutmeg, and salt.
Slowly pour in the melted butter, mixing with a fork until it turns crumbly.
Pour the topping mixture over the plums. Gently move it around with your hands until it evenly covers the plums. It's okay if the plums are not completely covered.
Bake, uncovered, for 40 minutes.
Remove from oven and let cool for at least 10 minutes before serving.
Store any unused portion in the refrigerator.