Combine first 4 ingredients in a medium bowl, stirring with a whisk.
Heat an 8-inch nonstick skillet over medium-high heat. Add 1 teaspoon oil to pan; swirl to coat. Stir in onion, bell peppers, thyme, and ham; sauté 4 minutes or until vegetables are crisp-tender. Remove vegetable mixture from pan; set aside. Clean pan.
Return pan to medium-high heat. Add 1 teaspoon oil to pan; swirl to coat. Add half of egg mixture to pan, tilting pan to spread evenly; cook 1 minute or until edges begin to set. Lift edge of omelet with a rubber spatula, tilting pan to roll uncooked egg mixture onto bottom of pan. Repeat procedure on opposite edge of omelet. Cook 1 minute or until center is just set. Sprinkle 2 tablespoons cheese evenly over omelet. Sprinkle half of vegetable mixture over cheese. Run spatula around edges and under omelet to loosen it from pan; fold in half. Slide omelet onto a plate. Repeat procedure with remaining oil, egg mixture, cheese, and vegetable mixture.
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