Blend the cottage cheese and egg until completely smooth. The protein in the cottage cheese and egg gives gluten free dough the structure it needs, so the biscuits rise tall and stay tender instead of gritty.
Whisk the gluten free flour, baking powder, baking soda, sugar and salt in a large bowl. Grate the frozen butter into the flour on the large holes of a box grater and toss to coat.
Pour in the cottage cheese mixture and stir with a fork until a soft dough forms, adding milk 1 tablespoon at a time only if it looks dry. Cover the bowl and refrigerate for 10 minutes so the flour fully hydrates, and preheat the oven to 425°F.
Turn the dough onto a sheet of parchment dusted with gluten free flour and pat it into a rectangle about 1 inch thick. Use the parchment to lift and fold the dough in half, pat it out again and repeat once more.
Pat the dough to 1 inch thick and cut out 2 1/2-inch rounds, pressing straight down without twisting. Place them on a parchment-lined baking sheet so they touch, which helps them rise up instead of out.
Bake for 16-20 minutes, until tall and golden brown. Brush the tops with melted butter right away and let them cool for 5 minutes before serving.