Before making the cookie dough, remove the ice cream from the freezer to soften. Also prepare the flax egg.
In a standing mixer combine the flour, room temperature vegan butter, cane sugar, flax eggs, and vanilla extract and beat until a thick batter is formed. Next, fold in ½ cup of the rainbow sprinkles and all the chocolate chips.
Line an 8*8 inch with parchment paper so that the parchment paper is hanging off the sides of the pan and completely covering the inside. Take half of the cookie dough and press it into the pan until completely flat. Top the layer of dough with the ice cream and smooth completely. Add to the freezer until the ice cream is completely firm again, about 15-20 minutes.
Take the remaining dough and add on top of the ice cream using your hands or a spatula to flatten, making sure to not squish out the ice cream. Add back to the freezer for 15-20 more minutes until sandwiches are completely frozen. Sandwiches can also also be left in the freezer overnight and cut the next day.
Remove the pan from the freezer and carefully lift the parchment from the pan. Use a large knife (ideally the length of cookies) to cut the cookie sandwiches into 9 even squares. Trim the edges of the outer slices if needed. Top the slices with the additional ¼ cup of rainbow sprinkles and enjoy.