Preheat oven to 250 degrees. Finely grind blanched almonds in food processor or blender. Combine almonds with almond oil, sugar, and beaten egg whites. Knead mixture into a firm dough. With moistened hands form dough into balls about the size of walnuts (about 1" in diameter). Place balls 1 inch apart on a baking sheet covered with baking parchment.
Place baking sheet in oven, and cook for 45-50 minutes. Transfer baked cookies to a wire rack . Using a fine sieve, dust cookies with confectioners sugar.

Yields about 40 cookies.