Mix the wet ingredients with sugar and matcha. In a large glass bowl, combine the oil, eggs, vanilla, granulated sugar, and sifted matcha powder in a bowl and whisk together until combined.
Melt the white chocolate. In a separate small bowl, melt the white chocolate. You can either microwave the chocolate in 15-second increments and mix until completely melted or you can use the double boiler method. If you opt for melting via a double boiler, fill a small saucepan about 1/3 of the way with water and place a heat-proof bowl filled with the white chocolate on top, making sure the water doesn't hit the bottom of the bowl. Place on the stove over medium-high heat and stir with a rubber spatula until the chocolate has melted. Cool the chocolate and set it aside.
Combine white chocolate with wet ingredients. When the white chocolate is cool/warm to the touch, add the melted white chocolate to the egg mixture and stir to incorporate.
Whisk the dry ingredients. In a medium mixing bowl, whisk the flour, baking powder, baking soda, and salt until combined.
Combine the wet and dry ingredients. Slowly pour the dry ingredients into the wet ingredient mixture and mix with a rubber spatula until combined. The batter should be thick and sticky.
Cover and chill in the refrigerator. Cover the batter with plastic wrap with the plastic wrap film touching the batter to prevent a film from forming and chill in the refrigerator for at least 1-2 hours or until firm.
Prepare the oven. Preheat the oven to 350 F and prepare a parchment or slipat lined baking tray.
Prepare a bowl of powdered sugar and assemble the cookies. Remove the dough from the fridge and use a tablespoon or a small ice cream scoop to form 1.5 inch balls. Roll the balls to make them smooth. Try to do this quickly as the dough can be a little sticky. If the dough is too sticky place it back in the refrigerator to chill a little longer. Dip each dough ball into the powder sugar and coat well. Double or triple coat with powdered sugar if necessary. Place the coated dough balls onto a lined baking sheet about 2 inches apart. Gently flatten the balls with your fingers to form even about 1/2 inch thick discs.
Bake at 350F for 10-12 minutes or until slightly golden along the edges. Let the cookies cool on the baking sheet for 3 minutes before transferring to a wire rack.