Pulse the 1 cup old-fashioned rolled oats, 1-¼ cups egg whites, and 1 cup cottage cheese briefly in a blender, don't overblend!. Let sit 15-20 minutes to hydrate. It will thicken noticeably. This is what makes the oats disappear.
Stir the ¼ cup honey into the ¼ cup warm water in a large bowl using a wooden or stainless spoon. Add the 2 tsp active dry yeast and let sit 5 minutes until foamy.
Pour the soaked oats mixture and the 2 tbsp salted butter and 2 tsp salt into the bloomed yeast and stir. Add the 3 cups bread flour and mix with a wooden spoon until a shaggy dough forms.
Knead with a dough hook 6-8 minutes, or by hand 10-12. Add the ½ cup bread flour a tablespoon at a time only as needed, until the dough pulls from the sides and feels like an earlobe. You may not use it all, it's a rather wet dough.
Oil a clean bowl, turn the dough to coat, cover, and let rise in a warm spot until doubled. The oven with just the light on works great.
Punch down and shape into a log by rolling it out into a wide rectangle then fold the long sides over about 2-3 inches, then roll it up like a log from the short side (the video is very helpful here!). Place seam side down in a greased 9x5 loaf pan, cover, and let rise until the dough crowns about an inch above the rim. (Or split between two pans for more normal-size loaves.)
Preheat to 350°. Beat the 1 large egg and brush the top. Bake 60-75 minutes (or less for 2 smaller loaves), tenting with foil for the last 35 if the top is golden early. Done at 190° internal. It rises a ton in the oven!
Turn out onto a rack immediately and cool completely before slicing. Cutting it warm will gum the crumb. Slice into 10 thick slices.