Cook and stir green peppers, onion, garlic, 1/2 teaspoon salt and the thyme in 1 tablespoon of the oil in 10-inch skillet over medium heat until green peppers are crisp-tender, about 8 minutes.
Add tomatoes; heat until hot, about 2 minutes.
Drain excess liquid from vegetables; place vegetables on platter.
Heat remaining oil in same skillet over medium heat until hot.
Mix remaining ingredients; pour into skillet.
Cook uncovered, over low heat, stirring frequently, until eggs are thickened throughout but still moist, 3 to 5 minutes.
Mound scrambled eggs in center of vegetables.
Sprinkle with snipped parsley if desired.