In a large Dutch oven or soup pot, brown the ground beef until cooked through leaving some large chunks, drain. Alternately, crumble four (quarter-pounpreviously grilled hamburgers and set aside.
Add the butter to the Dutch oven and cook over medium heat until melted. Add the celery, carrots and onion and sauté until crisp tender, about 10-12 minutes. Add garlic and cook for another minute or until fragrant. Add the potatoes, chicken broth, salt and pepper. Bring the soup to a boil. Reduce the heat slightly, and simmer uncovered for 20-25 minutes or until potatoes are tender.
In a small bowl whisk the cornstarch into 1 cup of the milk (or half-and-haluntil blended. Gradually stir the slurry into the soup. Bring it to a boil again and cook for another 2 minutes, stirring constantly, until thickened.
Reduce the heat to medium-low and slowly add the shredded cheddar cheese and the remaining cup of half-and-half. Cook and stir gently until the cheese is melted. Add the cooked ground beef and heat the chowder until steaming but not boiling. Check the seasoning and add salt and pepper as needed.
Serve immediately garnishing each bowl as desired.