Leftover Pork Frittata - Testing

https://www.food.com/recipe/pork-carnitas-frittata-219179

1 - The flavors are good, but the instructions made for a tough omelet. I've replaced them with the instructions I use for the Tomato Chèvre Omelette. Ergo, the next time I make this will be a test to see if these instructions work for this particular omelet. Ah. I just realized this is a frittata. I suspect I'd prefer it as an omelet, therefore I shan't change a thing!

3⁄4 cups pork, sliced thin into 1 by 1/2 inch strips (leftovers works great)
1 small onion, chopped 
2 garlic cloves, minced
3 Tbsps butter, divided
Juice from 1⁄2 lime
6 large eggs
1⁄3 cup water
3⁄4 teaspoons salt
1⁄4 cup shredded cheddar cheese
small handful cilantro leaf, chopped
1⁄4 cup fresh tomato, seeded and chopped

1. Sauté in 2 Tbsps of butter the onion for about 3 minutes then add the pork and continue to sauté until the onion is soft. Add the lime juice, remove from the heat and set aside.
2. Over medium heat, melt the remaining Tbsp of butter with the oil in a 10" oven-proof fry pan or omelette pan.
3. Whisk eggs with the salt and pepper until frothy.
4. Pour eggs into the hot pan. While cooking, lift the egg and tilt the pan to let uncooked egg get underneath.
5. With the oven rack at the mid-way setting, start the broiler (or use a salamander if you're so lucky to have one).
6. Spread the onion and pork mixture cheese across the surface of the omelette, then do the same with the cheese.
7. With the egg still uncooked on the surface, (not just slithery but actually jiggly), slip the pan into the oven and broil.
8. When the egg is set and the edges puff up a little, take it out of the oven and carefully fold the omelette. Sprinkle with the cilantro and the tomato and let rest about 5 minutes.
9. To serve, cut into segments to share.