Preheat oven to 180C (350F). Line the bottom and the sides of a 8-inch (20cm) round cake pan with parchment paper.
Prepare the filling: cut the plums in half, remove the pit, then cut each half into 3-4 pieces. Transfer the plums into a large bowl and add sugar, lemon zest and cornstarch. Mix well and set aside.
Make the crumble: in a large bowl, mix oats, flour, salt, sugar and baking powder. Add softened butter and rub with your fingertips until the mixture resembles crumbs.
Assemble the cake: spread half of the crumble on the bottom of the pan. Using a spoon or the bottom of a glass, press evenly the mixture. Them spread the filling on top of the crust. And sprinkle the remaining half of the crumble on top.
Bake for 30-35 minutes.
Release from the pan and serve with vanilla ice cream.