1/3 cup plus 1/2 cup sugar
1/4 cup water
1 tablespoon fresh lemon juice
1 teaspoon cornstarch
10 oz blueberries (2 cups)
1 cup all-purpose flour
1 3/4 teaspoons baking powder
1 teaspoon salt
1 large egg
1/2 cup whole milk
1 stick (1/2 cup) unsalted butter, melted and cooled slightly
1 teaspoon vanilla
Put oven rack in middle position and preheat oven to 375°F. Butter a 9-inch square baking pan.
Stir together 1/3 cup sugar with water, lemon juice, and cornstarch in a small saucepan, then stir in blueberries. Bring to a simmer, then simmer, stirring occasionally, 3 minutes. Remove from heat.
Whisk together flour, baking powder, salt, and remaining 1/2 cup sugar in a medium bowl.
Whisk together egg, milk, butter, and vanilla in a large bowl, then add flour mixture, whisking until just combined.
Spoon batter into baking pan, spreading evenly, then pour blueberry mixture evenly over batter (berries will sink). Bake until a knife inserted into center of cake portion comes out clean, 25 to 30 minutes. Cool in pan on a rack 5 minutes.
Cake can be made 1 day ahead and cooled completely, uncovered, then kept, wrapped well in foil, at room temperature.
Makes 6 to 8 breakfast or dessert servings.