Preheat Oven: Preheat to 350°F (175°C). Grease and flour two 8-inch cake pans or line with parchment paper.
Mix Dry Ingredients: In a medium bowl, sift together flour, baking powder, and salt. Set aside.
Cream Butter and Sugar: In a large bowl, beat the softened butter and sugar until light and fluffy.
Add Eggs and Zest: Add eggs one at a time, beating well after each. Stir in the lemon zest and vanilla extract.
Combine Dry and Wet Ingredients: Alternate adding dry ingredients and milk to the butter mixture, starting and ending with dry ingredients. Mix gently to avoid overmixing.
Add Lemon Juice: Fold in the fresh lemon juice until just combined.
Bake: Divide batter evenly between the pans. Bake for 25–30 minutes, or until a toothpick inserted in the center comes out clean.
Cool: Let cakes cool in pans for 10 minutes, then transfer to a wire rack.
Prepare Glaze: Whisk powdered sugar with lemon juice and heavy cream/butter until smooth. Pour over cooled cake. Garnish with extra zest if desired.