Preheat oven to 350°F. Spray three 6-inch (or two 8-inch) round cake pans with nonstick spray. Line with parchment paper and spray again.

Whisk together flour, baking powder, and salt. Set aside.

Combine sugar, oil, eggs, lemon extract, zest, and lemon juice. Mix on medium speed with an electric mixer until smooth.

Add half of flour mixture and half of the milk. Mix until just blended. Repeat with remaining flour and milk.

Divide batter evenly among cake pans and bake 22-25 minutes, or until golden and a toothpick inserted into the center comes out clean. Let cakes cool in pans for 5 minutes, then transfer to a wire rack to cool completely.

Cream butter on medium-high speed with an electric mixer until smooth and creamy. With mixer running, add shortening a little bit at a time until completely incorporated. (This helps prevent lumps.)

Add lemon extract, cardamom, and half of powdered sugar. Mix on low speed until mostly combined, then medium-high speed until completely combined. Repeat with remaining powdered sugar. Mix on medium-high speed 1 additional minute.

Use a serrated knife or a cake saw to cut off domed tops of cakes so that cakes are even and smooth. Place one cake layer on a plate or cake stand. Spread frosting over cake. Repeat with the next two layers.

Optional: Spread a thin crumb coat over the cake and chill for 20 minutes.

Spread frosting over outside of cake and garnish as desired.