Mix the flaxseed meal and water in a small bowl. Chill in the refrigerator for 5 minutes until the mixture thickens into a gel-like consistency.

Preheat the oven to 375°F (190°C) and line a baking sheet with a silicone mat or parchment paper.

Whisk the flour, baking soda, salt, and matcha powder in a large bowl. Ensure you break up any small clumps of baking soda or matcha so the color and leavening are evenly distributed.

Mix the oil and sugar in a separate medium bowl with a spatula until well combined. Stir in the thickened flax egg, milk, and vanilla extract.

Create a well in the center of the dry ingredients and pour in the wet mixture. Fold with a spatula until no dry flour is visible—the dough will be quite thick.

Scoop the dough into equal portions and shape them into balls. Place them on the baking sheet about 3 inches apart, then flatten each ball until they are roughly 2 inches in diameter.

Bake for 12 minutes for chewy cookies, or 15 to 16 minutes if you prefer them crisp.

Transfer the cookies to a wire rack and let them cool for 10 minutes. They will continue to firm up as they sit; serve once they have set.