In a mixing bowl, whisk together flour, then sift in cake flour and add baking powder and salt. Whisk 20 seconds, set aside.
In the bowl of an electric stand mixer, fitted with the paddle attachment, whip together butter and sugar until creamy and slightly pale and fluffy, about 1 - 2 minutes. Mix in eggs one at a time, then blend in vanilla.
With mixer set on low speed, slowly add in dry ingredients and mix until combined. Divide dough into two equal portions, shape each into a disk and cover with plastic wrap. Chill 3 hours or up to overnight.
Preheat oven to 375 degrees. Dust a clean working surface with a fair amount of flour, remove one dough from refrigerator, unwrap and place on floured surface. Sprinkle top with flour and roll to 3/8-inch thickness (right between 1/2-inch and 1/4-inch).
Cut into 2 1/2-inch rounds then transfer to a Silpat or parchment paper lined baking sheet. Bake in preheated oven 7 - 9 minutes (cookies won't become golden so don't over-bake. You want them slightly set but they should still make an indentation when touched).
Remove from oven and allow to cool on baking sheet 2 minutes, then transfer to a wire rack to cool completely. Repeat process with remaining dough. Once cookies are cool, frost with Lemon Cream Cheese Frosting. Decorate with diced fruit just before serving.
For the Lemon Cream Cheese Frosting:
In the bowl of an electric stand mixer, fitted with the paddle attachment, whip together butter, cream cheese and lemon zest until smooth and fluffy.
Mix in lemon juice, vanilla, and lemon extract. Add powdered sugar and whip mixture several minutes longer until fluffy.
Notes
*I recommend using berries (strawberries, raspberries, blueberries, blackberries, huckleberries, etc), kiwi, pineapple, peaches or mangos and dicing fruit into small pieces (except kiwis - slice those).