Preheat your Oven to 350˚F. Line a cookie sheet with parchment paper. In the bowl of your mixer with the paddle attachment, cream together your softened butter, 8 oz small-curd cottage cheese and the zest of one lemon. Mix on Medium/high speed for about 5 minutes until the mixture is smooth and fluffy.
Sift in the flour and baking powder (or whisk together flour and baking powder instead of sifting) and knead it together with your dough hook or by hand until your dough is soft and not sticking to your fingers. If you find it is still sticking to your fingers, add another Tbsp of flour.
Roll the dough into a ball and then roll it out on a smooth, non-stick surface until it is 1/4" thick. Use a round cookie cutter to cut out your cookies, cutting as many as you can out of your dough. Pour your sugar into a flat plate. Dip one side of your cookie into the sugar and gently pat it down to coat generously with sugar.
Fold it in half with the sugar on the inside. Dip one of the folded sides of your cookie in the sugar again and fold it in half with the sugar on the inside. When you fold, the sugar will always be on the inside. If you accidentally dip both sides of your cookie in sugar (I did a couple times) don't panic, it will still be edible. Place the finished cookies on the baking sheet, fairly close together, since they don't expand very much.
Make a ball of dough out of the remaining scraps and roll it out again and again until you've used up all of your dough. Bake at 350˚F for 32-35 minutes or until the edges and tops are golden brown.