Preheat oven to 350°F/175°C. Line a cookie sheet with parchment paper.
Place the butter in a mixing bowl. Use either a handheld or stand mixer on medium speed and beat until light and fluffy. Add the sugars and beat again until fluffy. Add the flax, water, and vanilla and beat to combine.
In a separate bowl, stir together the flour, cornstarch, baking soda, baking powder, and salt. Pour the flour mixture into the butter mixture and stir to combine. This is a thick dough. But if it's still crumbly, add a tablespoon of water and stir that in.
Add most of the chocolate chips and dried cranberries and stir until combined. Reserve some chocolate chips and cranberries to place on the top of cookies. Cover and refrigerate the dough for up to an hour.
Drop by rounded spoonful about 2 inches apart on the prepared cookie sheet. Add more cranberries and chocolate chips to the top of each cookie dough ball. Bake for 9 minutes, (or up to 11 minutes depending on your desired final cookie texture). If you prefer chewier cookies, remove them at 9 minutes. If you prefer crispier, cook for a few minutes longer. See note.
Once the cookies are done, remove them from the oven and allow them to cool for a minute or two on the cookie sheet before transferring them to a wire rack to cool completely.
Store baked cookies in an airtight container.