Preheat the oven to 350°F. Grease and lightly flour a 9x13-inch baking pan.

In a medium bowl, whisk together 2 1/2 cups flour, the baking powder, baking soda, and salt.

In a large bowl, beat the softened butter and granulated sugar for 2–3 minutes, until pale and fluffy.

Add the eggs one at a time, beating well after each addition.

Mix in the vanilla extract and buttermilk. The mixture may look slightly curdled.

Add the flour mixture in two additions, mixing just until combined after each one.

Stir in the lemon zest and lemon juice.

Toss the blueberries with the remaining 1 tablespoon flour, then fold them gently into the batter.

Spread the batter evenly in the prepared pan.

Bake for 35–40 minutes, until a toothpick inserted in the center comes out clean and the edges begin pulling away from the pan.

Let the cake cool completely for at least 1 hour before frosting.

For the frosting, beat the softened butter until pale and fluffy.

Add the cream cheese and blueberry jam, then beat until smooth.

Add the powdered sugar gradually, mixing well after each addition.

Beat in the vanilla extract, then continue beating for 1–2 minutes until light and fluffy.

Spread the frosting evenly over the cooled cake before slicing and serving.