Melt 1 teaspoon butter in omelet pan or skillet. Add green pepper; saute 2 to 3 minutes, until tender. Add ham; saute 1 minute to heat through. Remove to small bowl; keep warm.
In another small bowl, lightly beat together eggs, water, chives, salt if using, and pepper.
Heat remaining butter in same pan. Pour in egg mixture, which should set immediately at edges. Using inverted pancake turner or spatula, carefully push cooked portions at edges toward center so uncooked portions can reach hot pan surface, tilting and moving pan as necessary. Continue until egg is set and will not flow, about 30 seconds.
Sprinkle the ham filling on one side of the omelet; sprinkle with Parmesan cheese. Fold the uncovered half of the omelet over to cover the filling. Then invert the omelet onto plate.