In a large bowl or stand mixer, cream butter and sugar on a medium speed. Add in the egg and vanilla extract until incorporated.
In a medium bowl combine flour, salt, baking powder, and baking soda. Turn the speed down to low. Slowly start to add dry ingredients to wet ingredients. Mix until dough starts to form. Place in refrigerator for 30 minutes or up to one day.
Cut the dough in half. Cover a cutting board with a tablespoon of flour and place dough on the cutting board. Use a rolling pin to roll out the dough to a 1/4 inch thick. Use a 4-inch round cookie cutter to cut the cookies. Do the same to the other half of the dough.
Preheat oven to 350°F. Put parchment paper over a cookie sheet and bake for 15 minutes or until edges are a light brown. Let the cookies cool down before decorating.
In a medium bowl or stand mixer, beat together the cream cheese and butter on a medium speed until smooth. Add in powder sugar and milk. Beat for about a minute. Add in vanilla extract and lemon zest. Beat for another minute.
Frost the cookie and arrange fruit in a decorative pattern. Leftovers can be stored in an airtight container up to 2 days.