Wash and cut the Yukon Gold potatoes into evenly sized pieces to ensure they cook evenly. Fill a large pot with water, add a generous pinch of salt, and bring it to a boil. Add the potatoes and cook them until they’re about 90% tender. You’ll know they’re ready when you can pierce them with a fork but they don’t fall apart. This should take about 10 minutes. Drain the potatoes and set them aside while you prepare the gravy.

Heat a large skillet over medium heat and melt the butter. Add the bacon grease for an extra depth of flavor. Sprinkle in the flour a little at a time, whisking constantly to create a smooth roux. Let the mixture cook until it turns golden brown and smells nutty. Gradually pour in the chicken broth, whisking continuously to avoid lumps. If the gravy seems too thick, add more broth a little at a time to reach your desired consistency. Season the gravy with salt and pepper, then reduce the heat to a gentle simmer.

Stir the chopped onions into the gravy, ensuring they’re well-coated. Cook until the onions begin to soften, about 3-5 minutes. Gently fold in the partially cooked potatoes, being careful not to break them. Stir everything together and let the potatoes simmer in the gravy for about 10 minutes.Taste and adjust the seasoning as needed. Keep the potatoes warm on low heat while you prepare the eggs.

In a mixing bowl, whisk the eggs with milk (if using), salt, and pepper until fully combined. Heat a nonstick skillet over medium heat and melt the butter. Pour the egg mixture into the skillet, letting it sit undisturbed for a few seconds. Use a spatula to gently stir the eggs, scraping the bottom of the pan to create soft curds. When the eggs are nearly set, sprinkle in the shredded cheese. Stir until the cheese is melted and the eggs are creamy. Remove from heat.