In a small bowl beat egg yolks and pepper on high speed of electric mixer about 5 minutes, or until thick and lemon-colored. In a medium bowl beat egg whites and water until stiff peaks form. Pour yolks over whites and gently fold in.
Preheat oven to 325°F. In a 7-inch nonstick skillet with ovenproof handle melt butter over low heat. Lift and tilt skillet to coat sides. Pour egg mixture into hot skillet, mounding it slightly higher around edges. Cook over low heat about 6 minutes, or until eggs are puffed and set and bottom is golden brown. Bake for 6 to 8 minutes, or until a knife inserted near center comes out clean.
Meanwhile, in a small skillet heat chicken broth. Cook and stir bell pepper and spinach in broth for 2 minutes. Stir in tuna and oregano; season to taste with salt and pepper. Drain; keep warm. Loosen sides of omelet with spatula. Make a shallow cut across omelet, cutting slightly off center; fill with tuna mixture. Fold smaller portion of omelet over larger portion. Sprinkle with cheese. Serve immediately.