Preheat your oven to 350°F (175°C). Grease three 8-inch round cake pans and line the bottoms with parchment paper.

In a medium bowl, whisk together the sifted flour, baking powder and salt. Set aside.

In a large bowl, beat the softened butter and sugar on medium speed for 3–4 minutes, until pale, light and fluffy. Scrape down the bowl once or twice.

Add the eggs one at a time, beating well after each one. Then mix in the lemon zest and vanilla extract.

Stir the lemon juice into the milk. It may look slightly curdled — that's normal.

With the mixer on low, add the flour mixture in three parts, alternating with the milk mixture in two parts, starting and ending with the flour. Mix only until no dry flour remains.

Divide the batter evenly between the pans and bake for 22–25 minutes (or 28–32 minutes in two 9-inch pans), until a toothpick inserted in the center comes out clean or with a few moist crumbs. Cool completely before frosting.

Beat the softened cream cheese and butter on medium speed for about 2 minutes, until smooth and creamy with no lumps.

Turn the mixer to low and add the powdered sugar a little at a time, mixing until fully combined. Add the lemon juice and vanilla and beat until light and spreadable.

Place the first cake layer, spread a smooth layer of buttercream, add the second layer and frost it, then add the top layer and cover the whole cake with frosting.

Pipe decorative swirls on top and finish with fresh lemon slices.