In a 10-inch nonstick or well-seasoned ovenproof skillet cook mushrooms and onion in margarine or butter over medium-high heat about 5 minutes or until tender but not brown. Add zucchini; cover and cook over medium-low heat 2 to 3 minutes, stirring occasionally. Stir in ham. Beat eggs until blended but not foamy. Stir in thyme, caraway seed, salt, and pepper.
Pour egg mixture over vegetables. Cook over low heat, without stirring, until mixture begins to set on the bottom and around the edge. As eggs set, run a spatula around the edge of skillet, lifting egg mixture to allow uncooked portion to flow underneath. Continue cooking and lifting edge until mixture is almost set. Sprinkle with cheese. Broil 5 inches from heat for 1 to 2 minutes or until eggs are just set and cheese is melted. Sprinkle with chives. To serve, cut into wedges; serve from skillet. Makes 4 to 6 servings.