Prepare the egg replacer according to package instructions. If using a flax egg, combine 1 Tbsp ground flax + 3 Tbsp warm water in a small bowl. Set aside.
In a medium mixing bowl, whisk together the flour, baking soda, and salt. Set aside.
In a stand mixer set to medium speed, cream together the sugar, brown sugar, and vegan butter until light and fluffy and well combined.
Add the sourdough discard, the egg replacer, and the vanilla and mix on medium speed until just combined.
On low speed, slowly add the dry ingredients until the ingredients are just combined and the dough begins to pull away from the side of the bowl.
Add the chocolate chips and rolled oats and continue to mix until just incorporated.
Cover the bowl with plastic wrap and refrigerate for at least 1 hour, up to 24 hours.
When ready to bake, preheat oven to 375℉.
Roll cookies into 1¼" balls and place on a 9x13" cookie sheet in a 3x4 formation.
Bake at 375℉ for 15 minutes. The cookies should be lightly golden.
Allow cookies to cool on a wire rack at least 5 minutes before serving.