
Blueberry Pudding Cake
['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.
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