Preheat oven to 350 degrees. Line baking sheets with parchment paper. In medium bowl, sift together flour blend, cinnamon, ginger, baking powder and salt. Set aside. In bowl of stand mixer, beat together powdered sugar, molasses, coconut oil, coconut milk and vanilla until smooth. Add flour mixture and continue to mix for 1-2 minutes. Use hands to knead dough until it comes together. Form into two discs and wrap in plastic wrap. Refrigerate dough for 1 hour.
On counter, lay out large piece of plastic wrap. Place one disc of cookie dough in the center and top with another piece of plastic wrap. Roll with rolling pin until dough is about 1/4″ thick. Cut dough using gingerbread man cookie cutter or desired shape. Carefully place cookies on prepared baking sheets (place dough back in refrigerator if it gets too soft to work with). Bake for 7-8 minutes. Remove cookies from oven and place on cooling rack to cool completely.
While cookies are cooling, make simple icing. Mix together powdered sugar and 2 tablespoons coconut milk. Stir until smooth. Add more coconut milk as needed. Place glaze in piping bag with small, round tip or use Ziploc bag, cutting the tip. Pipe onto cooled cookies. Allow icing to sit for 1 hour to harden.