Step 1: Preheat your oven to 350°F (175°C) and line two large baking sheets with parchment paper or silicone mats.
Step 2: In a large bowl, cream together the softened butter and powdered sugar until light and fluffy, about 2-3 minutes.
Step 3: Stir in the vanilla extract until well combined.
Step 4: Sift the all-purpose flour, matcha powder, and salt into the wet ingredients. Mix on low speed until a soft dough forms.
Step 5: Scoop about 1 tablespoon of dough at a time and roll into smooth balls. Place them 2 inches apart on the prepared baking sheets.
Step 6: Use your thumb or the back of a 1/2 teaspoon measuring spoon to gently press an indentation into the center of each ball.
Step 7: Bake for 10-12 minutes, or until the bottoms are very lightly golden. Do not overbake; you want to preserve the green color.
Step 8: While the cookies bake, prepare the filling by melting white chocolate chips with heavy cream in 20-second intervals in the microwave, stirring until smooth.
Step 9: Once the cookies are out of the oven, gently re-press the centers if they puffed up. Let them cool completely on a wire rack.
Step 10: Spoon or pipe the white chocolate ganache into the centers of the cooled cookies. Let the filling set before serving.