Melt 0.5 tbsp butter in a 10-inch nonstick skillet over medium heat until foamy, about 30 seconds. Add the onion and red bell pepper and cook, stirring occasionally, until crisp-tender, 3β4 minutes.
Stir in the garlic and ground cumin and cook until fragrant, 30 seconds. Add the diced green chiles and cook to warm through, 30 seconds. Transfer the vegetable mixture to a plate.
Wipe out the skillet. Add the remaining 1 tbsp butter and melt over medium-low heat, 30β60 seconds. Whisk the eggs with the water, kosher salt, and black pepper until smooth and lightly frothy, 15β20 seconds, then pour into the skillet.
Using a spatula, stir the eggs gently for 10β15 seconds to form small curds, then let cook undisturbed until the bottom is just set and the top is still slightly wet, 1β2 minutes.
Scatter the warm vegetable mixture and the diced tomato over one half of the omelette. Sprinkle the pepper jack cheese evenly over the same half. Fold the bare half over the filling and cook until the cheese is melted and the center is just set, 1β2 minutes.
Slide the omelette onto a warm plate and rest 30 seconds. Serve with salsa, avocado, and cilantro to taste.