Preheat oven to 375˚ F.
Combine flour, sugar, baking powder, baking soda, and salt in a food processor bowl with steel blade and blend for 8 seconds.
Add finely chopped eggs and pulse 10 to 12 times to incorporate.
Cut butter and lemon zest into flour mixture by pulsing 8 to 10 times until mixture resembles a coarse meal.
Combine lemon juice and milk and add to mixture. Pulse just until dough is evenly wetted and begins to come together.
Turn dough onto a lightly floured surface (It will appear somewhat mealy until pressure is applied). Pat into 8-inch circle, approximately ½ to ¾ inch thick. Cut into 6 to 8 wedges. (For mini scones pat into two 4-inch circles.)
Place on parchment lined or butter baking sheet. Brush tops of scones with milk and sprinkle with sugar if desired.
Bake 12 to 15 minutes or until golden brown. Serve scones warm with lemon butter.
Combine butter with powdered sugar and lemon zest; beat until creamy. Gradually beat in lemon juice. Cover and refrigerate until ready to serve.