Preheat oven to 350°F (175°C). Grease and flour a 12-cup mini muffin tin, or line with mini muffin liners.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, ensuring each is incorporated before adding the next.
Stir in the lemon zest and vanilla extract.
In a separate medium bowl, whisk together the sifted all-purpose flour, baking powder, and salt.
In a small bowl, whisk together the milk and ¼ cup fresh lemon juice.
Alternately add the dry ingredients and the wet ingredients to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined. Do not overmix.
Spoon the batter evenly into the prepared mini muffin cups, filling each about two-thirds full.
Bake for 18-22 minutes, or until a wooden skewer inserted into the center of a cake comes out clean.
Let the cakes cool in the tin for 5-10 minutes before transferring them to a wire rack to cool completely.

Prepare the Lemon Glaze: In a small bowl, whisk together the sifted powdered sugar and 2 tablespoons of lemon juice until smooth. Add more lemon juice, a teaspoon at a time, if needed to reach desired drizzling consistency.
Drizzle the glaze over the cooled mini cakes.