Begin by placing softened butter in a large mixing bowl. Beat it together with confectioner's sugar until light and fluffy, about 3–4 minutes.

Mix in the vanilla extract until fully combined. Gradually add in cornstarch, all-purpose flour, and matcha powder, mixing on low speed.

Divide the dough into two portions, wrap in plastic wrap, and chill in the refrigerator for at least 2 hours.

Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.

Roll out one portion of the chilled dough to about 1/3 inch thick. Use cookie cutters to shape the cookies.

Bake for approximately 12 minutes, or until edges are set. Allow to cool on the baking sheet for 2 minutes.

Combine chocolate chips and vegetable oil in a bowl, microwave until melted and smooth.

Dip cooled cookies halfway into the melted chocolate, let excess drip off, and place on parchment paper. Dust with matcha powder.

Let cookies sit at room temperature until the chocolate is set.