Combine filling ingredients in 7- to 10-inch nonstick omelet pan or skillet.
Cook and stir over medium heat until water has evaporated and vegetables are
crisp-tender, 3 to 4 minutes.
Remove from pan; keep warm. Clean pan.
Beat eggs, 1/4 cup water, cheese, basil and garlic powder in medium bowl
Heat butter in same pan over medium-high heat until hot. Tilt pan to coat
bottom. Pour in 1/2 of the 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.
Place 1/2 of the filling on one side of the omelet. Fold omelet in half
with turner and slide onto plate; keep warm.
Repeat with remaining egg mixture and filling to make second omelet.