Preheat the oven to 350°F (175°C).

Grease and flour two 9-inch round cake pans.

In a medium bowl, whisk together 1 ½ cups all-purpose flour, 1 ½ teaspoons baking powder, and ½ teaspoon salt.

In a separate bowl, beat ½ cup softened unsalted butter and 1 cup granulated sugar until light and fluffy.

Add 2 large eggs, 1 tablespoon fresh lemon zest, and 1 teaspoon vanilla extract to the butter mixture and mix until well combined.

Gradually add the dry mixture to the creamed mixture, alternating with ½ cup milk, mixing just until combined.

Stir in 3 tablespoons fresh lemon juice until the batter is smooth.

Divide the batter evenly between the prepared pans and bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake layers to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.