Dice the onion into small, even pieces and chop the leftover turkey into bite-sized bits. Crack the eggs into a bowl and whisk until just frothy and combined.
Heat the skillet over medium heat and add the butter. Once melted and bubbling, add the diced onion and cook for 2-3 minutes, stirring occasionally, until the onion becomes golden and fragrant.
Push the onions to one side of the pan and pour the beaten eggs into the empty space. Let them sit undisturbed for about 10 seconds, then gently scramble with a spatula, moving slowly to create soft curds. Cook until eggs are just beginning to set, about 30 seconds.
Add the shredded turkey to the eggs and stir gently to combine. Continue cooking for 1-2 minutes, until the eggs are fluffy and cooked through, with the turkey heated evenly throughout.
Sprinkle the shredded cheese evenly over the scramble and cover the skillet briefly to let the cheese melt, about 30 seconds. If desired, add a dash of hot sauce or herbs at this stage for extra flavor.
Remove the skillet from heat and let the scramble rest for a moment. Finish by stirring in chopped herbs and seasoning with salt and pepper. Serve immediately, garnished with additional herbs if desired, and enjoy the warm, cheesy, smoky flavors.
