Whisk the flour, gingerbread spice, baking soda and salt in a medium bowl. Beat the butter, brown sugar and molasses in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Reduce the mixer speed to medium low and add the flour mixture in two batches, beating until just combined. Divide the dough between 2 large pieces of plastic wrap. Flatten into disks and wrap. Refrigerate until firm, at least 2 hours or overnight.
Position racks in the upper and lower thirds of the oven; preheat to 350˚. Line 2 baking sheets with parchment paper. Roll out 1 disk of dough on a lightly floured surface until about 3/8 inch thick. Cut out trees using 2- to 3-inch cutters. (If the dough becomes too sticky, refrigerate 15 minutes.) Arrange the cutouts 1 inch apart on the prepared pans.
Bake, switching the pans halfway through, until the cookies are puffed and the edges are lightly set, 15 to 18 minutes. Let cool 5 minutes on the pans, then remove the cookies to racks to cool completely.
Roll out the other disk of dough on a lightly floured surface and cut out more cookies. Once the baking sheets have cooled, arrange the cutouts on the pans, bake and let cool.
Make the icing: Whisk the confectioners' sugar with the water until smooth and very thick. Transfer the icing to a resealable plastic bag, snip off a corner and pipe on the cookies; sprinkle with sanding sugar. Decorate with the sunflower seeds.