Whisk the eggs and water together in a bowl for a full minute. Season with salt and pepper, whisk again, and set aside.
Heat a nonstick skillet over medium heat and add the oil. Once hot, add the jalapeños, onion, and tomato. Sauté for about 2 minutes until softened. Transfer to a bowl and set aside.
Wipe the pan clean with a paper towel and return it to low heat for a full minute. Add the butter and let it melt, then pour in the egg mixture. Let it sit undisturbed for about 1 minute.
Using a spatula, gently push the eggs in a few spots toward the center so the uncooked egg flows underneath. Keep doing this until the top is just barely set, not runny, but still a little glossy.
Scatter the sautéed vegetables over one half of the omelet, then add the cheese on top. Fold the empty half over the filling and cook for 30 seconds to 1 more minute.
Optional: flip the omelet and cook for a few more seconds, then add a little more cheese on top.
Slide onto a plate. Add a dash of hot sauce, sprinkle chopped cilantro, warm flour or corn tortillas, sliced avocado and tomatoes on the side.
Notes
Adding water to eggs ensures the omelet is light and fluffy.