Preheat oven 350F
Prepare flax egg. In a small bowl add ground flax seed and water whisk and let sit for at least 5 minutes.
Add white sugar, brown sugar, salt and baking powder. Beat until well combined.
Beat in milk, flax egg* and vanilla until combined.
Beat in as much flour as you can using the hand mixer the stir in the rest until dough is formed. Divide in half and roll into balls.
Place each half between two sheets of parchment paper. Roll the dough out until it is 1/4 inch thick (I prefer to roll it out a little thicker). Once rolled out place the the refrigerator for at least 15 minutes. This gives the dough time to cool and which makes it easier to cut out and hold their lovely shape in the oven.
Line two baking sheets with parchment paper. Once the dough is chilled, cut out the cookies and lay them on the parchment lined cookie sheet. Re-roll remaining dough until all of the dough is used.
Bake cookies for 12-14 minutes or until edges are firm. Use an oven thermometer to make sure oven is heated to 350F. Cool cookies on a wire rack.
In a mixing bowl combine vegan butter, milk, vanilla, salt and powdered sugar. Beat ingredients until smooth. Frost cookies once the cookies are completely cooled.
*after letting the flax egg sit for 5 minutes whisk well before adding to the mixture.
*you may want to add more milk if frosting is too thick to spread.