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.