In a stand mixer bowl fitted with a paddle attachment, add in the butter and sugar. Beat until light and fluffy, about 2-3 minutes.
Add in the beaten egg and vanilla extract and continue to beat until everything is incorporated.
Sift in the flour and matcha and fold with a spatula until just combined. Be careful not to overmix.
Dump the mixture onto a large piece of plastic wrap or parchment paper and form dough into a disc. Wrap up the disc tightly with the plastic wrap/parchment paper and place into the fridge for at least 1 hour.
Preheat oven to 350°F/177°C.
Using a rolling pin, roll out the chilled dough to ¼″ inch thickness and cut out shapes using a small 1 ½" round cookie cutter.
Place the cut-out cookies onto a baking sheet lined with parchment paper. Bake the cookies at 350°F/177°C for 10-12 minutes.
Remove and cool the cookies on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.
Make the strawberry buttercream filling:
In a stand mixer bowl fitted with a paddle attachment, cream together the softened butter and icing sugar until light and fluffy, about 4-5 minutes on medium high speed.
Add in vanilla extract.
Fold in the freeze-dried strawberry powder with a spatula.
If you prefer a stronger pink hue, you can add a touch of strawberry extract/food colouring.
Fill a piping bag with the strawberry buttercream fitted with a plain round tip.
Pair the cookies according to size with one facing up and one facing down.
Pipe a large dollop of strawberry buttercream into the middle of the cookies facing up and place it's corresponding cookie over top. Press down firmly and let it firm up in a cool place.
Cookies can be enjoyed after the buttercream has firmed up. Store in an airtight container in the fridge if not consuming right away.