Place plum slices in a large bowl. Add sugar, brown sugar, and lemon juice and toss to combine. Let sit about 30 minutes, while you make the crumble.
In the bowl of a stand mixer fitted with the paddle attachment, combine buckwheat flour, oats, sugar, cinnamon, cardamom, and salt. Mix on low speed for 30 seconds to combine.
Add cold butter to flour mixture and mix on medium speed until butter is evenly distributed and completely incorporated. (If making ahead of time, the crumble mixture can be stored in the refrigerator for up to three days.)
Add cornstarch to plums and stir to incorporate.
Preheat oven to 350° F. Divide fruit evenly among four small ramekins (or place in a 10” cast iron). Top with each with a thick layer of buckwheat crumble.
Bake for 35-40 minutes until fruit is bubbly and topping is golden brown. Let cool slightly and serve warm with ice cream.