Preheat oven to 375 degrees and set rack at middle level in oven.
Break the almond paste into 1-inch pieces. In the bowl of a mixer, combine almond paste, and sugars. With the paddle attachment, mix on the slowest speed to crumble together, paste and sugars. Pour in the egg whites in 3 to 4 additions, beating well between each addition.
Scrape down the bowl frequently as you are adding the egg whites.
If possible, leave time to pack the macaroon paste into a plastic container and allow it to age overnight in the refrigerator before baking.
Use a plain tube with a 1/2 to 3/4-inch opening (Ateco #7 or #8) to pipe 3/4 to 1-inch macaroons on parchment or waxed paper lined cookie trays. Leave 1-inch around each macaroon.
Moisten the surface of the macaroons with a wet towel and sprinkle with granulated or confectioners' sugar. Bake immediately for 15 minutes to 20 minutes, until thet are well puffed and golden. Cool the macaroons. When cool, remove them from paper by turning paper over and moistening the back of the paper, then peel it off.