Brown the beef. In a large pot or Dutch oven over medium heat, cook the ground beef, breaking it into small crumbles with a spoon, for 6 to 8 minutes, until no pink remains and it reaches an internal temperature of 160°F (71°C). Drain off excess fat, transfer the beef to a plate, and set aside.

Sauté the vegetables. In the same pot, melt 2 tablespoons of the butter over medium heat. Add the onion, carrot, and celery, and cook for 5 to 6 minutes, stirring occasionally, until the onion turns translucent and the vegetables start to soften.

Simmer the potatoes. Add the diced potatoes and chicken broth to the pot. Bring to a boil, then reduce to a simmer and cook uncovered for 12 to 15 minutes, until the potatoes are fork-tender.