These look like the real thing, but they taste a lot better: thin, crisp, and sweet.
Cream the butter, gradually beating in the sugar, egg yolk, and vanilla. Mix the flour and salt, slowly stirring the dry ingredients into the creamed. Gather the dough into a ball, then flatten it onto a large sheet of plastic wrap. Wrap the dough, slip it into a plastic bag, and refrigerate for at least 4 hours, or until firm.
When the dough is thoroughly chilled, let it sit at room temperature for about 15 minutes, or until it can be rolled. Preheat oven to 350 degrees F and lightly grease two large cookie sheets.
Roll the dough about ⅛ inch thick on a sheet of waxed paper or plastic wrap. Cut dough into 2- or 2-¼-inch rounds and place them onto the sheets, leaving about 1-½ inches between each one. (Gather the scraps and reroll them, too.) Brush cookies lightly with egg white, then arrange 5 almond slices on each cookie, like the spokes of a wheel. Brush again with egg white, very lightly, then sprinkle each one with a little sugar. Bake for 10 to 12 minutes; they should start to brown, especially around the edges. Briefly cool the cookies on the sheets, then transfer to a rack and finish cooling.