In a small bowl stir together 1.5 tbsp ground flax and 2.5 tbsp water. Let it sit for 5 minutes. This will be our "flax egg" and serve as a binder.
In a large bowl cream 1/2 cup butter. Then add the "flax egg" mixture, 1/2 cup sugar, 1/4 cup brown sugar, and 1 tsp vanilla. Beat until creamy.
In a medium bowl stir together these dry ingredients: 1.75 cups flour, 1 tsp baking powder, 1/2 tbsp corn starch, 1/2 tsp baking soda, and 1/4 tsp salt.
Add dry ingredients to wet ingredients, and add 1 tbsp non-dairy milk. Stir together with a spoon or spatula until combined. Take care to not over-mix. The dough should feel fairly wet.
Put the dough into the medium bowl and place in the refrigerator for at least 15 minutes. I like to go ahead and scoop the dough balls and roll them and place them in the fridge on a baking sheet. You can also opt to use a large cookie scoop to make your cookie dough balls.
Preheat oven to 350 degrees.
Put parchment paper on a cookie pan. Place cookie dough balls onto the parchment paper. Bake at 350 degrees for 10-12 minutes. The cookies will be very soft coming out, but they will firm up to the perfect texture after cooling for 10-15 minutes.
Let cookies cool on cooling rack completely before icing or frosting.