In a large pot or Dutch oven, brown the ground beef over medium-high heat, breaking it up as it cooks. Drain any excess fat.

Add the diced onion and minced garlic to the pot and sauté until the onion is translucent, about 5 minutes.

Add the diced potatoes and chicken or beef broth to the pot. Bring the mixture to a boil, then reduce the heat and simmer for 15-20 minutes, or until the potatoes are tender.

In a separate saucepan, melt the butter over medium heat. Whisk in the all-purpose flour and cook for 2-3 minutes, stirring constantly, to create a roux.

Gradually whisk the milk into the roux, stirring continuously until the mixture thickens, about 5 minutes.

Add the thickened milk mixture to the pot with the potatoes and ground beef. Stir to combine and let the soup simmer for an additional 10 minutes, or until the desired consistency is achieved.

Season with salt, pepper, and dried thyme to taste.