SAUTÉ pepper mixture in 1 tsp. butter in 6- to 8-inch nonstick omelet pan or skillet over medium-high heat until tender, about 2 minutes. REMOVE from pan; KEEP warm. CLEAN pan.
BEAT eggs, water, salt and pepper in small bowl until blended. HEAT remaining 1 tsp. butter in same pan over medium-high heat until hot. TILT pan to coat bottom. POUR in egg mixture. Mixture should set immediately at edges.
Gently PUSH cooked portions from edges toward the center with inverted turner 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 with turner; SLIDE omelet into bun.