Preheat the oven to 170°C/340°F. Grease and line a 9-inch/23-centimeter round pan with parchment paper.
Make the crumble by pulsing the cold butter, sugar, and flour in a food processor until coarse crumbs form. Set aside.
Make the batter by creaming the very soft butter with sugar in a stand mixer or by hand until smooth. Add the oil and eggs and beat briefly until combined. Add the flour, baking soda, baking powder, milk, sour cream, vanilla, and salt and mix just until the batter is smooth and slightly thick.
Pour the batter into the prepared pan. Scatter the blueberries evenly over the batter, then sprinkle the crumble evenly on top.
Bake until the top is golden and a tester inserted in the center comes out clean or with a few moist crumbs, about 40–50 minutes. Cool the cake in the pan on a wire rack for 20 minutes, then remove, cool completely, and dust with powdered sugar if using. Slice and serve.