Preheat the oven to 425°F and line a baking sheet with parchment paper. Blend the cottage cheese and honey in a blender or food processor for about 1 minute, until completely smooth and creamy, then refrigerate while you prepare the dry ingredients.
Whisk the flour, baking powder, baking soda and salt in a large bowl. Grate the frozen butter directly into the bowl on the large holes of a box grater, tossing every few seconds so the shreds stay coated in flour and separate.
Pour the blended cottage cheese over the flour mixture and stir with a fork just until a shaggy dough forms. If dry flour remains at the bottom of the bowl, add the milk 1 tablespoon at a time until the dough barely holds together.
Turn the dough onto a lightly floured surface and pat it into a rectangle about 1 inch thick. Fold it into thirds like a letter, turn it 90 degrees and pat it out again.
Repeat the folding 3 more times. These folds create the tall, flaky layers, so work quickly to keep the butter cold. Finish by patting the dough to an even 1 inch thickness. Cut out biscuits with a 2 1/2-inch round cutter, pressing straight down without twisting so they rise tall. Gently press the scraps together once to cut the last biscuits, place them on the baking sheet so they just touch, and chill for 10 minutes.
Bake for 14-17 minutes, until the biscuits are tall and deep golden brown. While they bake, stir together the melted butter and honey for the honey butter.
Brush the hot biscuits generously with the honey butter as soon as they come out of the oven and sprinkle with flaky sea salt. Let them rest for 5 minutes and serve warm.