Heat oven to 350° F. Place the potatoes in a large pot, add enough cold water to cover by 1 inch, and bring to a boil. Add 1 teaspoon salt, reduce heat, and simmer until tender, 15 to 18 minutes. Drain and return the potatoes to the pot; add the milk, butter, ½ teaspoon salt, and ¼ teaspoon pepper and mash.
Meanwhile, heat 1 tablespoon of the oil in a 5- to 6-quart Dutch oven over medium-high heat. Add the onions and cook, stirring often, until beginning to soften, 4 to 6 minutes; transfer to a medium bowl.
Heat the remaining tablespoon of oil in the Dutch oven. Add the beef, ½ teaspoon salt, and ¼ teaspoon pepper and cook, breaking the beef up with a spoon, until no longer pink, 4 to 6 minutes; mix in the tomato paste and Worcestershire sauce. Sprinkle with the flour and cook, stirring, for 1 minute. Add the broth, squash, peas, and onions and bring to a simmer.
Transfer the beef mixture to a 9-by-13-inch or some other 3-quart baking dish and top with the potatoes.
Bake until the potatoes are lightly golden, the filling is bubbling, and the squash is tender, 40 to 45 minutes. Let cool for 5 minutes before serving.
Not amazing, but tasty comfort food; the squash is a nice touch. An easy way to feed a large group.