Chorizo, a spicy Spanish or Mexican sausage, is easy to find in most supermarkets. Be sure to use soft chorizo, not dry cured, for this recipe.
In a mixing bowl, dress arugula with 1 tablespoon olive oil and season with salt and pepper. Place rolls in a warm oven to heat.
Heat remaining olive oil in a skillet over medium-high heat and cook chorizo until lightly browned, about 3 to 4 minutes. Remove from heat and set aside to cool. In a mixing bowl, whisk eggs until combined. Fold in parsley, cheese, cream, 1 teaspoon each of salt and pepper, and chorizo.
Heat ½ tablespoon butter in a skillet until hot. Pour ½ cup of the egg mixture into the skillet. Cook until omelet is set–not jiggly, but still moist. Fold one-third of the omelet in toward the center, then fold in half and remove from the skillet. Repeat with remaining butter and egg mixture for a total of four omelets.
To assemble, remove rolls from the oven. Spread 1 tablespoon Smoky Mayonnaise on each bread half. Place ½ cup arugula, two Roasted Tomatoes, and one omelet in the center of each roll.
Smoky Mayonnaise Pimenton or Spanish paprika is available at gourmet markets or online at tienda.com.
Combine all ingredients in a small bowl. Refrigerate until ready to use.
Heat oven to 275°. Place tomatoes on a baking sheet and drizzle with olive oil, then season with salt and pepper. Bake 2-½ to 3 hours, or until reduced in size by half, but still slightly moist. Remove, cool, and reserve. Tomatoes can be made up to 2 days in advance and kept in the refrigerator.