Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper or wax paper (don’t use aluminum foil).
In a medium bowl, whisk together the dry ingredients (flour, matcha powder, baking soda, and salt). Set this aside for a moment.
In a large bowl, cream the butter and sugar together until the mix is light and fluffy. You can use a stand mixer fitted with a paddle attachment or an electric hand mixer; it'll take about 3-5 minutes on medium speed.
Next, beat in the egg and vanilla extract to the butter mixture until well incorporated.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until the dough comes together. Don't overmix, or you'll end up with tough cookies.
If time allows, let the mix rest in the fridge for at least 2 hours before proceeding to the next step - if you don’t have the time, you’ll just make somewhat more cakey cookies.
Once rested, scoop single tablespoonfuls of dough, roll them into balls, and place them on your prepared baking sheet about 2 inches apart – they'll spread a bit. If you need to use two baking sheets, you can place them on two different racks in the preheated oven.
Bake for 10-12 minutes, or until the edges are just starting to turn golden. They might still seem soft in the center, but they'll firm up as they cool.