Cover two heavy aluminum cookie sheets with parchment paper.
Put the almonds and sugar in the work bowl of a food processor fitted with the metal blade. Process just until the mixture is smooth. Don't overprocess! Immediately add the egg whites, before the almonds lose their oil. Pulse about 10 times. Add the vanilla and pulse 2 or 3 times. You should be able to just shape the batter with your hands. The batter should be sticky and quite thick, like rough, sticky clay. The size of the eggs used and the amount of oil in the almonds determines the consistency, so be prepared to add a bit more almonds or egg white.
Shape the batter into balls the size of walnuts. Arrange on the parchment covered baking sheets. Brush each macaroon with a bit of water. For variety, either sprinkle with sugar or put an almond in each, and bake for 16 minutes, or until lightly brown. Remove the cookie sheets from the oven, cool on the parchment, on racks. Cool completely and store, tightly covered, at room temperature for a week. These freeze very well. Each recipe makes about 40 2-inch diameter cookies.