Heat 1 tablespoon oil in medium-size skillet. Add onion; cook until almost tender, 10 minutes. Add vinegar, 1/4 teaspoon salt and sugar; cook until onion is tender, browned and liquid evaporates, 5 minutes. Remove onion to bowl. Wipe skillet.
Heat 1 tablespoon oil in skillet. Sprinkle remaining salt on steak.Add steak to skillet; cook over medium-high heat 10 minutes for medium-rare, turning once. Transfer to cutting surface. Let stand 10 minutes. Cut steak at 45 degree angle across grain into 1/8-inch-thick slices.
Meanwhile, cut each loaf crosswise in half; slice each half horizontally lengthwise. Brush inside of bread with remaining 1 tablespoon oil; sprinkle with oregano and thyme. Place on baking sheet.
Bake in heated 400 degree F oven until lightly toasted, about 5 minutes.
Layer bottom halves of bread with lettuce. Top with steak slices, onion rings and Salsa Mayonnaise. Makes 4 servings.
Combine tomato, mayonnaise, onion, ketchup, jalapeño pepper, cilantro, lime juice and 1/8 teaspoon salt. Refrigerate, covered, until using.