In a medium bowl, mix together the flour, salt, powdered sugar and matcha.
In another bowl, beat the softened butter with an electric hand mixer, just until it becomes soft. Beat in the vanilla. Then gradually mix in the dry ingredients. Everything should form a single mass. If it stubbornly remains a powdery bunch of crumbs, sprinkle in one or two teaspoons of water, and continue to mix. When everything is combined, you will have a beautiful green dough.
Cut it in half, form each half into a disc and wrap in plastic. Refrigerate for about 30 minutes. Longer than this and you may have to let it warm up a bit so it can be worked.
Preheat oven to 350ºF. Lightly flour your surface and a rolling pin, place a disc on the table, and roll it out to about a quarter-inch thickness. I cut these cookies into little rectangles, then used a spatula to move them onto parchment or waxed paper on a baking sheet. These cookies don’t spread out much in the baking, so can be pretty closely spaced on the baking sheet. Once they are all set out on the baking sheets, sprinkle lightly with the confectioner’s sugar.
Slide the baking sheets in the oven and bake for 10 to 12 minutes or so, depending on the neurosis level of your oven. They should lightly brown around the edges.
Cool the cookies on the baking sheets for 5 minutes, then completely on a rack. Only after they are cooled should you try to dip them.
For dipping, chop the chocolate, then melt it in the top of a double boiler until it is shiny and liquid. To dip the cookies, hold by one end, then dip the other end, gently shake off the excess and place on waxed paper on a rack or plate. Once the cookies are set, which will take a while, store them in an airtight container with waxed paper between the layers. Done. The cookies will keep for a week or more.
If you wish, you can also skip the chocolate entirely and just serve these in their delicate, elegant simplicity.