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Preheat the oven to 350 °F (top/bottom heat). Line the square pan (9 × 9 in) with parchment paper.
Mix flour, baking powder, and salt in a bowl.
In a second bowl, whisk together sugar, eggs, and vanilla with the oil. Stir in yogurt and milk.
Fold in the flour mixture until a smooth batter forms.
Prepare the blueberry jam: bring blueberries, sugar, and lemon juice to a boil in a small pot. Simmer for 5–6 minutes until the berries burst. Thicken with the dissolved cornstarch, boil briefly again, then let cool and strain through a sieve.
Spread half of the batter into the pan and smooth out. Evenly spread the blueberry jam on top, then add the remaining batter and spread again. Lightly swirl with the handle of a spoon or a fork to create a pretty pattern.
Bake for about 35–40 minutes, until a toothpick (inserted only into the cake, not the jam) comes out clean.
Let the cake cool in the pan, cut into squares, and lightly dust with powdered sugar.