Roast the poblano pepper directly over an open flame or under the broiler until the skin is blistered.
Remove from the heat and place in a paper bag for 10 minutes.
Peel the skin off the poblano and slice into strips.
In a large bowl, whisk together the eggs, heavy cream, and a pinch of salt and pepper.
Ensure the mixture is thoroughly combined for a fluffy consistency.
Heat a non-stick skillet over medium heat and pour the egg mixture into the pan.
Cook until the edges begin to set, then add roasted poblano, serrano pepper, shredded beef, and cheese.
Fold one side of the omelette over the filling and cook for an additional 1-2 minutes.
This step helps to melt the cheese and heat the ingredients thoroughly.
Slide the omelette onto a plate and garnish with avocado slices and a dollop of sour cream.
Enjoy the dish while hot for the best flavor.