Beat the softened butter using a mixer; if using a stand mixer, use the paddle attachment.
Stop mixing to add in the powdered sugar (lest you have a sugar explosion).
Beat again until ingredients are fully incorporated. Then add in extract and milk or cream.
Scrape down the sides of the bowl and resume beating until the buttercream has doubled in volume.
To frost the lemon cake in a semi-naked style, I recommend using a 6" cake board, a turntable, and an offset spatula. Place the cake board on top of the turntable.
Add a smear of buttercream on the cakeboard and place one layer of cake on top. Add about 1/3-1/2 cup frosting on top of that layer. Smooth out with the offset spatula, turning the cake as needed to get a flat surface.
Repeat with the other two layers of cake.
You should now have three layers of cake with a 1/4-1/2 inch layer of frosting on top of each one. Using the offset spatula, smooth any excess frosting sticking out from in between your layers along the sides of the cake.
Holding your spatula flat against the side of the cake with one hand, slowly spin the turntable with the other hand in order to get a smooth surface.
If there are any spots of cake along the sides that look too rough, simply add smears of frosting and repeat the previous step until the sides are smooth. Alternatively, you could also use a bench scraper instead of an offset spatula to smooth the sides.
Finish decorations to your liking! I used a pile of blueberries on top and a few sprigs of rosemary on the bottom.
This cake stays good covered at room temperature. If you have a lot of exposed cake that is not covered in frosting, I recommend putting your cake in the fridge to let the frosting crust. Then press plastic wrap directly on top of your cake to prevent it from drying out.