Cut the bacon crosswise in 1-inch slices. Cook the bacon in an 8-inch ovenproof saute pan over medium-low heat for 5 to 7 minutes, stirring occasionally, until browned. Drain the bacon on paper towels and discard the fat from the pan. Add the butter to the pan, and then add the potato and yellow onion. Cook over medium-low heat for about 10 minutes, tossing occasionally, until the onion starts to brown and the potato is tender but firm. Add the jalapeno pepper and cook for 30 seconds.
Meanwhile, in a medium bowl, beat the eggs, milk, salt, and pepper together with a fork. Stir in the scallions and diced Cheddar. When the potato is cooked, add the bacon to the pan and pour over the egg mixture. Place the pan in the oven for 15 to 20 minutes, until the omelet puffs and the eggs are almost cooked in the center. Sprinkle with a handful of grated Cheddar and bake for another minute. Serve hot directly from the pan.