Chop peppers. Saute peppers in 1 teaspoon butter in a medium-sized skillet over medium-high heat until tender, about 2 minutes. Remove from pan.

Whisk eggs, 1 tablespoon of water (not in list), salt and pepper in small bowl until blended. Heat remaining 1 teaspoon butter in same pan over medium-high heat until hot. Pour in egg mixture. Mixture should set immediately at edges. Carefully push cooked portions from edges toward the center so that uncooked eggs can reach the hot pan surface. Continue cooking, tilting pan and gently moving cooked portions as needed.

When top surface of eggs is thickened and no visible liquid egg remains, spoon peppers down center of omelet; top with cheese. Fold omelet sides in; slide omelet into bun. Cut in half.  Serve with pears.