Preheat your griddle to 400°F, then add butter and a little oil to the surface.
If you're using raw bacon or sausage, cook it first. If you're using diced ham or pre-cooked meat, you can add that later with the veggies.
Toss your hash browns in the butter and oil, then spread them out into a thin, even layer. You want them thin, but not so thin that you can see the griddle underneath.
Season the potatoes with salt and pepper, then let them cook undisturbed for about 10 minutes, or until the edges start to turn golden brown.
While the hash browns cook, sauté your meat (if not already cooked) and diced veggies on another part of the griddle.
Slowly pour the beaten eggs directly over the cooked hash browns, spreading them out evenly with back of spatula.
Layer the cooked meat, veggies, and cheese on top of the eggs.
Cut the rectangle in half, then carefully fold each half over to form two separate omelets.
Serve hot—I like mine with sour cream, salsa, or a splash of hot sauce.