Ready the oven and pan. Heat the oven to 350 degrees F with the rack in the middle. Grease an 8 inch springform pan and line the bottom with parchment paper. Whisk the custard base. Whisk the milk, vanilla bean paste, 1/3 cup sugar, yolks, and cornstarch in a saucepan until no lumps remain.
Thicken the custard. Cook over medium low heat, whisking nonstop for 4 to 5 minutes, until the custard is thick like pudding.
Add the butter. Off the heat, whisk in the cold butter until melted, then let the custard cool while you mix the batter.
Mix the batter. Whisk 1/2 cup sugar, oil, and egg for 1 minute, then add the yogurt, vanilla extract, and zest. Fold in the flour, baking powder, and salt just until combined, then fold in the blueberries.
Layer and bake. Spread the batter in the pan and top with the custard. Bake for 50 minutes, until the top is golden and a toothpick inserted near the edge comes out clean.
Cool. Let the cake cool in the pan for 1 hour, then release the springform and serve slightly warm or chilled.