Preheat the oven to 375°F. Grease a 12-cup muffin tin or line with paper liners and set aside.
Place the cottage cheese in a blender or food processor and pulse until mostly smooth but still a little textured (about 20–30 seconds). This step lightens the curds so the muffins have a fine, tender crumb.
In a large bowl whisk the eggs, milk and melted butter together until combined. Stir in the whipped cottage cheese until evenly mixed.
In a separate bowl whisk the flour, baking powder, salt, and black pepper. Pour the dry ingredients into the wet mixture and stir with a spatula just until no dry streaks remain—don’t overmix.
Fold in the shredded cheddar and chopped chives, saving a little cheddar to sprinkle on top if you like. Let the batter rest for 10 minutes; this hydrates the flour and yields taller, moister muffins.
Spoon the batter into the prepared muffin cups, filling each about three-quarters full. Sprinkle the reserved cheese on top of a few muffins for extra color.
Bake at 375°F for 20 minutes, rotating the pan once halfway through for even browning. The muffins are done when tops are golden and a toothpick inserted into the center comes out with a few moist crumbs.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to finish cooling slightly. Serve warm or at room temperature.