Preheat oven to 350°F. Linke a cookie sheet with parchment paper.
Prepare the flax egg. Set aside.
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 molasses, vinegar, and flax egg. Beat to combine.
In a separate bowl, stir together the flour, baking soda, baking powder, spices, and salt. Pour the flour mixture in with the butter mixture and stir to combine. This is a thick dough. But if it's crumbly, add a tablespoon of water and stir that in.
Add most of the chocolate chips and stir until combined. Reserve some chocolate chips to place on the top of unbaked cookies.
Drop by rounded spoonful about 2 inches apart on the prepared cookie sheet. Add more chocolate chips to the top of each cookie dough ball and sprinkle with coarse sugar. Bake for 9–11 minutes. If you prefer chewier cookies, remove them at 9 minutes. If you prefer crispier, cook for a few minutes longer.
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 to a wire rack to cool completely.
Store baked cookies in an airtight container.