First, make your flax egg. Combine the flaxseed meal and water. Stir to combine and place in the fridge for 5 minutes or until thickened and congealed.
While the flax egg sets, brown the butter over medium heat, stirring constantly until the butter begins to foam and turns a golden brown, emitting a nutty aroma. Make sure you only brown the butter lightly. When butter browns the liquid evaporates off which can dry out your dough. As soon as the butter starts to turn brown and smell nutty, take it off the heat to prevent any more liquid from escaping. Take butter off the heat and allow to cool.
In a large mixing bowl combine the cooled brown butter, brown sugar, and white sugar. Beat until mixed together. Add in the flax egg, milk, and vanilla extract. Mix well.
In separate bowl mix together the flour, salt and baking soda. Mix half the dry ingredients into the wet until everything comes together. Slowly add in the remaining flour a little bit at a time, stopping if the dough starts to get too dry. Fold in the chocolate.
Enjoy!
Notes
To temper the all purpose flour for the cookie dough filling, line a baking sheet with parchment paper and preheat the oven to 325°F. Spread the flour out into an even layer. Place in the oven and bake for 2 minutes, take the flour out and use a rubber spatula to stir the flour. Repeat this process for 15 minutes or until the flour has reached 165°F. Remove the flour for the oven and allow to cool before using in the cookie dough filling.