Stir the ground flaxseed and warm water together, then let the mixture thicken for 5 minutes. Heat the oven to 350 degrees F and line two baking sheets with parchment paper.
Whisk the flour, cocoa powder, baking soda, and salt together in a medium bowl.
Beat the vegan butter, brown sugar, and granulated sugar until creamy. Beat in the flaxseed mixture and vanilla extract, then mix in the dry ingredients just until a dough forms.
Divide the dough into 16 equal balls and flatten each one into a 2 1/2-inch round. Bake for 9 to 11 minutes, then cool the cookies completely.
Let the mint ice cream soften for about 10 minutes. Stir in the mini chocolate chips, working quickly so the ice cream remains thick.
Place a generous scoop of mint ice cream on the flat side of eight cookies. Top with the remaining cookies and press gently until the filling reaches the edges.
Arrange the sandwiches on a lined tray and freeze for 2 hours until firm.
Let the ice cream sandwiches stand at room temperature for 3 to 5 minutes before serving.
