Preheat the oven to 325ºF.
Sift the flour and toss it with the almond and sugar powder. Whip the egg whites in an electric mixer at low speed until they start to froth. If you are not whipping the whites in a copper bowl, then add the cream of tartar at this point. Gradually increase the whipping speed to medium-high, and continue whipping until the whites form very stiff peaks and just begin to slip and streak around the side of the bowl. Add the superfine sugar and continue whipping at high speed for a few seconds longer to incorporate the sugar and tighten the meringue. Gently fold in the almond and sugar powder and flour. Scoop the batter into the pastry bag, and pipe the batter in domes 1-inch wide, arranging them on the baking sheets in staggered rows and separating them by about 1-inch. Unless you have 2 ovens, pipe only 1 sheet of cookies at a time, and keep the remaining batter in the pastry bag until the first sheet is baked. Dust chopped almonds over the piped batter. Turn the baking sheet upside down and tap it with a wooden spatula to dislodge the excess almonds, then quickly turn the baking sheet right side up again. Dust with confectioners’ sugar. Let rest for about 1 minute to allow some of the confectioners’ sugar to dissolve. Bake, 1 sheet at a time, until the cookies are lightly browned on the bottom and dry and crusty on top, but still soft inside, about 15 to 18 minutes.
Place the baking sheet on a wire rack and let the cookies cool. While they are still warm and before the batter sets, carefully transfer them to a wire rack with a metal spatula. Then let them finish cooling on the wire rack. Press the center of each dome on the flat side with your fingertip to make a slight depression. Turn half the domes upside down and spoon about 1/2 teaspoon of apricot jam on the center of each. Then place a second dome right side up on top of each to make a sandwich. Lightly dust the balls with confectioners’ sugar, then turn them upside down and dust the other side as well.
Storage: Covered airtight in a tin cookie box or a cookie jar for up to 4 to 6 days. They look best if they are dusted with confectioners’ sugar shortly before serving.
Yield: about 30 cookies