Mix together 1 tbsp of flax meal with 2 1/2 tbsp of water (or another vegan egg replacer equal to 1 egg) and set aside.
In a medium-sized bowl, mix together 1/2 cup melted vegan butter, 1 cup sugar, and 1/2 cup sifted cocoa powder until incorporated.
Add the flax egg, 2 tbsp. milk, and 2 tsp. vanilla, then blend again until fluffy. (A hand mixer works great for this, or you can stir with a wooden spoon for about 2 minutes.)
Sprinkle in the dry ingredients (1 1/3 cup flour, 1 tbsp. cornstarch, 1/2 tsp. baking powder, and 1/2 tsp. salt), then mix until a thick dough forms and fold in the chocolate chips.
Scoop out about 2 tbsp of dough and place it on a cookie sheet. Press down to form the shape and thickness of the cookie that you want. (They won't spread too much during baking.)
Bake at 350°F (176 °C) for 10-12 minutes. Take them out of the oven and allow them to cool on the cookie sheet for about 10 minutes before removing them with a spatula. Allow cooking on the countertop or a cooling rack.
Notes
For best results, use stick margarine. Earth Balance sticks, Mikayo, Country Crock plant-based butter, or the stick version of my homemade vegan butter work best.
Melt the butter. Melted butter gives cookies a fudgy, chewy texture. If you want a cakier cookie, you can use softened butter instead.
Sift the cocoa powder. Cocoa powder tends to get clumpy, especially in humid climates. To avoid clumps of cocoa powder, use a sifter or a metal mesh strainer to break them up before adding the cocoa powder to the cookies.
Be sure to spoon-measure the flour. This ensures you don't pack the flour into the measuring cup and end up using too much in the recipe.