Preheat the oven to 350°F (180°C) and line a large baking sheet with parchment paper.

In a large mixing bowl, using a hand mixer, beat the softened butter with a hand mixer until smooth and creamy.

Add the sugar, egg, milk, and salt. Mix on medium speed until the mixture looks pale and fully combined.

In a separate bowl, sift together the flour, matcha powder and baking soda. Whisk well to evenly combine.

Add the dry ingredients into the wet mixture. Mix on low speed just until a soft, slightly sticky dough forms. Stop mixing as soon as no dry flour remains.

Scoop the cookie dough using a small cookie scoop or tablespoon (about 24 portions). Roll lightly between your palms to smooth them out.

Place dough balls onto the prepared baking sheet, spacing them 2 inches apart.

For flatter sandwich cookies, gently press each ball down to about ½ inch thickness.

Bake for 8–10 minutes, or until the edges look set. The centres should remain soft, as they firm up when they cool.

Cool for 5–10 minutes on the tray, then transfer to a wire rack to cool completely.

Melt the white chocolate in the microwave for 30 seconds. Stir, then microwave again in 15-second intervals. Keep repeating until fully melted. Let cool to room temperature.

Beat the cold butter in a medium bowl until pale and fluffy.

Add the cooled melted chocolate, cold cream cheese, and vanilla. Mix until just combined and smooth. Add to a piping bag and use immediately for best piping consistency.

Pair cookies by size and flip half of them upside-down.

Pipe or spread a generous layer of cheesecake filling onto the flat side of one cookie.

Top with the second cookie and gently press to create an even sandwich cookie.