Preheat the oven to 375°F (190°C). Lightly butter a 2–2.5 quart baking dish and set aside.

In a large bowl, toss the sliced plums with granulated sugar, lemon juice, cornstarch (or flour), fresh ginger, and 1 tablespoon of the chopped basil. Let the mixture rest for 10 minutes so the flavors bloom and the juices begin to release.

Make the topping: In another bowl, combine oats, flour, brown sugar, cinnamon, and a pinch of salt. Add the cold butter and blend with your fingers or a pastry cutter until the mixture resembles chunky wet sand with pea-sized clumps. If using, fold in the chopped nuts.

Spread the plum mixture evenly in the prepared baking dish. Sprinkle the crumble topping over the fruit, pressing down very lightly to help it form a cohesive crust while baking.

Bake for 30–40 minutes, until the fruit is bubbling and the topping is golden brown and crisp. The edges should pull slightly away from the dish as the juices thicken.

Remove from the oven and let rest for 10 minutes before serving. The sauce will thicken as it cools, and the aromas of ginger and basil will deepen beautifully.