Preheat oven to 325°F with racks positioned in upper middle and lower middle of oven. Prepare 2 baking sheets or inverted baking sheets by lightly greasing and placing a 12 x 15 piece of parchment on each. The spray holds the parchment in place and the parchment cut to this size is a guide to spreading the batter.
Combine ground ginger, flour, baking soda and salt in a bowl. (you can lightly toast the ground ginger by heating over medium heat in small pan about a minute but I think its fine without doing this)
With a mixer, on medium high speed, beat the butter and brown sugar until light and fluffy, around 2 to 3 minutes. Add fresh ginger and vanilla and mix until combined. Lower mixer speed to low setting, add 1/3 flour mixture at a time, alternating with 1/2 of the milk at a time, mixing well after each addition. (Begin and end with flour for a total of 3 additions of flour and 2 additions of milk).
Divide the batter evenly between the baking sheets (about 3/4 cup each). Using an offset spatula, spread the batter as evenly as possible near to the edges of the parchment paper. This is the step to take your time with and really try to get it even.
Place in the preheated oven and bake until golden brown, about 16 to 20 minutes, Rotating pans from front to back and switching racks halfway through baking.
Remove from oven and immediately score into 2 x 3 inch rectangles using a pizza wheel. Allow to cool completely and then gently separate cookies along score lines with the tip of a sharp knife.
Can be stored in an airtight container for up to 5 days.