Line three baking sheets with parchment paper. In a medium bowl, whisk together the flour, salt, and matcha. In a large bowl, beat the butter, granulated sugar, and honey with an electric mixer on medium speed until fluffy, 2 to 3 minutes. Reduce the speed to low, and gradually add the flour mixture, stirring until the flour is incorporated.
Divide the dough in half; place each half on a sheet of parchment paper and form into a 2-inch diameter log. Wrap the logs tightly and chill until firm, 3 to 4 hours.
Heat oven to 325°F. Slice the dough into 1/2-inch thick slices and space 1-inch apart on the prepared baking sheets.
Bake, rotating the baking sheets halfway through, until cookies are firm, about 12 minutes. Transfer to a wire rack to cool completely, then dust with powdered sugar.
