Fill a saucepan full of water, then season with a generous pinch of Kosher salt. Add peeled, cubed potatoes, then set over medium-high heat. Cook until the potatoes can easily be pierced with a knife with only slight resistance. Drain.
Whisk eggs in a mixing bowl with birria consommé, shredded Mozzarella, Kosher salt, and black pepper.
Preheat an oven. Heat unsalted butter and olive oil in a 10-inch nonstick skillet over medium-high heat. When hot, add diced red onion, reserving raw onion for topping the frittata (optional). Cook.
Add the shredded beef. Reserve the beef, then add the rest of the birria to the skillet. Stir, allowing this to heat through for a minute or two, then pour the beaten eggs on top. Bake until the eggs are completely set and have puffed up slightly.
Carefully remove from the oven, allow to cool slightly, then top with the reserved birria. Garnish with reserved diced red onion and lots of fresh chopped cilantro. Enjoy with lime wedges and sour cream, if wanted.