Heat oven to 450° F. In a large bowl, combine the turkey, bread crumbs, egg, onion, and 2 tablespoons each of the milk and ketchup; season with ½ teaspoon salt and ½ teaspoon pepper.
On a rimmed baking sheet, form the mixture into a loaf and top with the remaining ¼ cup ketchup. Bake until cooked through, 30 to 35 minutes.
Meanwhile, in a large saucepan, cover the potatoes with enough cold water to cover by 1 inch. Add 1 teaspoon salt and bring to a boil. Reduce heat and simmer until very tender, 20 to 25 minutes. Drain and return the potatoes to the pot. Add the butter, the remaining ½ cup of milk, and ¼ teaspoon pepper and mash to the desired consistency.
Bring a second large saucepan of water to a boil; add 1 tablespoon salt. Add the green beans and cook until just tender, 4 to 5 minutes. Drain and run under cold water to cool. Serve with the meat loaf and mashed potatoes.