Preheat oven to 350 degrees. Butter a 5 by 9 inch baking pan, and dust with flour, tapping out excess.
Combine 1/2 cup sugar and 1/2 cup lemon juice in a small saucepan over medium heat. Simmer, stirring occasionally, until sugar dissolves and syrup is thickened, about 4 minutes. Let stand while making cakes.
Meanwhile, combine heavy cream, remaining 2 tablespoons lemon juice, and the vanilla in a bowl. Whisk together flour, baking powder, baking soda, and 1/4 teaspoon salt in another bowl
Beat butter, lemon zest, and remaining cup sugar with a mixer on medium speed until pale and fluffy.
Reduce speed to low, and add eggs, 1 at a time, beating well after each addition.
Beat in flour mixture in 3 additions, alternating with cream mixture, beginning and ending with flour.
1 stick unsalted butter, plus more for pans
2 cups all-purpose flour, plus more for pans
1 1/2 cups sugar
1 tablespoon finely grated lemon zest, plus 1/2 cup plus 2 tablespoons fresh lemon juice (from 4 lemons)
3/4 cup heavy cream
1 teaspoon pure vanilla extract
1/4 teaspoon baking powder
1/4 teaspoon baking soda
2 large eggs
6 ounces blueberries (1 1/4 cups)