Combine tomato, green bell pepper, onion, and tarragon in a large bowl. Whisk eggs, milk, salt, and black pepper in another bowl. Melt butter in a skillet over medium heat. Cook and stir egg mixture in hot butter until nearly set, about 2 minutes. Stir vegetable mixture into eggs; continue to cook and stir until eggs are set and vegetables begin to soften, about 3 minutes more.