Preheat oven to 425 degrees. Heat a large (5-quart) heavy pot or Dutch oven over high. Cook beef, breaking up meat with a spoon, until no longer pink, 4 to 5 minutes. Add onion and garlic; cook until softened, about 4 minutes.
Add thyme, ketchup, and flour; stir until combined.
Add 1/2 cup water and vegetables. Cook until vegetables are warmed through and liquid has thickened, about 3 minutes. Season with salt and pepper.
Spoon beef mixture into a 2-quart baking dish. Spread potatoes evenly over beef; using a fork, decorate potatoes with lines and peaks. Place dish on a rimmed baking sheet, and bake until potatoes are lightly browned, 10 to 15 minutes. Serve.
Make filling; spoon into baking dish. Spread potatoes over top, and let cool completely. Cover with plastic wrap, and refrigerate up to 1 day. Preheat oven to 425 degrees; remove plastic wrap, and bake until potatoes are lightly browned, 30 to 40 minutes.