Preheat the oven to 375 degrees F (190 degrees C). Grease a 9 inch springform pan.
Stir flour, ½ cup sugar, and baking powder together in a medium bowl. Add butter, mixing until it resembles coarse crumbs. Stir in egg and 1 teaspoon of vanilla extract, then pat into the bottom of the prepared pan. Add blueberries.
Whisk sour cream, remaining ½ cup sugar, egg yolks, and remaining 1 teaspoon vanilla extract in another bowl until smooth. Pour over blueberries.
Bake until light brown, about 60 to 70 minutes. Run a knife around the edge once the cake is cool, then remove the outer ring before serving.