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Preheat an oven to 395 F (200 C). Beat the eggs together in a bowl and add chopped chives. Season generously with salt and pepper, and mix the ingredients well to combine.
Melt the butter in a large pan at medium heat and add the beaten egg. Allow the egg to settle a little before scrambling. Cook through until scrambled.
After the eggs have cooked, arrange a slice of ham for each roll-up on a clean sheet of parchment paper. Lay a slice of cheddar cheese over each slice of ham, evenly in the center. Now, turn back to your eggs.
Once the eggs are cooked, divide them into even portions. Add the eggs to the center of each slice of cheese, leaving a small gap around the edges for rolling. Make sure the eggs are no longer steaming before you roll them up.
Carefully roll each slice into a tight tube so that the edges overlap and the filling is secure inside. Spray a small baking dish with pan spray. Then, arrange the roll-ups side by side in the dish.
Transfer to the oven to bake for 10 minutes or until completely cooked through. The cheese should be melted and the ham browned and slightly crisp at the edges. Serve hot.