For the sugar cookie base, in the bowl of an electric mixer, cream together sugar, butter, egg, and lemon extract. Cream well. In a separate bowl, stir together baking soda, baking powder, flour and salt. Add flour mixture to wet mixture and mix just until combined.
Press mixture evenly into a lightly greased jelly roll or cookie pan and bake for approximately 10-12 minutes. Check at 10 minutes. Don't over-bake or they won't be soft. You'll want them to be just barely set but you don't want to see browning. Allow the bars to cool.
Make buttercream frosting by creaming together softened butter, powdered sugar and blueberry puree until creamy and fluffy. Mix at least two minutes. If after mixing for 2 minutes, you think it needs to be thinner, add milk a tablespoonful at a time, mixing in between, to thin. Mine was a perfect consistency without adding milk. Spread frosting over cooled bars, slice, and serve.