Cream butter, sugar, and salt
Add flour, matcha, and sesame seeds and mix until combined.
Roll dough into a log roughly 6 inches long. It should be 1.5-2 inches in diameter. Chill logs in the fridge until firm. (This dough can easily be chilled overnight or even stashed in the freezer for a later bake.)
When ready to bake, preheat oven to 350 degrees. Line a baking sheet with parchment paper or silicone.
Slice the ends off the log (you can still bake these). Slice the log into half-inch thick cookies. You should get 12 if your log was around 6 inches log, more if you rolled it thinner.
Arrange cookies on tray and bake for 10 minutes.
Let cookies cool to room temperature.
If dipping in chocolate, microwave chocolate and shortening in a heat-proof bowl in 15-20 second increments, stirring in between, until melted and smooth. This should only take about 45 seconds maximum.
Dip each cookie about 1/3-1/2 of the way into the chocolate, using a spoon to help spread the chocolate over the cookie. Set each cookie back on the tray or on a wire rack to let the chocolate harden. Store at room temperature and enjoy!