If you haven’t already, parboil the potatoes. Fill a saucepan about ⅔ full of water, then season with a generous pinch of Kosher salt. Add peeled, cubed potatoes, then set over medium-high heat. Cook for 10 minutes, or until the potatoes can easily be pierced with a knife with only slight resistance. Drain.
Whisk the eggs. Whisk 6 large eggs in a mixing bowl with ½ cup birria consommé, ⅔ cup shredded Mozzarella (reserve the remaining ⅓ cup), 1 tsp Kosher salt, and ¼ tsp black pepper.
Sauté onion. Preheat an oven to 350°F (175°C). Heat 2 Tbsp unsalted butter and 2 Tbsp olive oil in a 10-inch nonstick skillet over medium-high heat. When hot, add diced red onion, reserving 2 Tbsp raw onion for topping the frittata (optional). Cook, stirring occasionally, for 3 minutes.
Add potatoes. Add the cubed parboiled potatoes, season with ½ tsp Kosher salt, then cook, stirring occasionally, for another 3-5 minutes.
Assemble, then bake. Add the shredded beef. Reserve about ¼ cup of 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. Sprinkle with the remaining ⅓ cup of shredded Mozzarella, then transfer to the preheated oven. Bake for 10 minutes, or until the eggs are completely set and have puffed up slightly.
Garnish, then serve! Carefully remove from the oven, allow to cool slightly, then top with the reserved birria (I like to mount this in the center of the frittata). Garnish with reserved diced red onion and lots of fresh chopped cilantro. Enjoy with lime wedges and sour cream, if wanted.