Preheat the oven to 450 degrees F. Brush a baking dish with 1 tablespoon olive oil. Season the tomatoes and onion rounds with salt and pepper and add to the dish, cut-side up. Mix the remaining 2 tablespoons olive oil with the panko and sprinkle over the tomatoes and onion. Bake until tender and golden brown, 15 to 20 minutes.
Whisk the eggs, milk and herbs in a bowl; season with salt and pepper. Heat a small nonstick skillet over medium-high heat. Add 1 teaspoon butter, swirling to coat. When the foam subsides, add one-quarter of the egg mixture. Cook 10 seconds, then move a rubber spatula around the edge of the pan until the mixture is just set, about 1 minute. Scatter one-quarter of the cheese down the center, then fold the omelet in half. Cook about 30 more seconds, or to desired doneness. Transfer to a plate. Repeat to make 3 more omelets. Serve with the roasted tomatoes and onions.