In a large pot or Dutch oven over medium heat, cook the ground beef until browned. Drain excess grease if needed.
Stir in the diced onions, shredded carrots, and sliced celery. Cook for about 5 minutes, stirring occasionally, until the vegetables start to soften.
Pour in the beef broth and add the cubed potatoes. Bring to a boil, then reduce heat and let simmer for about 15 minutes, or until the potatoes are fork-tender.
In a separate saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute. Slowly add the milk, whisking continuously until thickened.
Pour the milk sauce into the soup pot and stir well. Stir in salt, basil, and pepper. Add the shredded cheddar cheese and mix until melted and smooth.
Remove from heat and stir in the sour cream. Adjust seasoning if needed.
Cheese Options: Mild cheddar works best, but sharp cheddar, Colby Jack, or a blend can be used for extra flavor.
Consistency Tips: For a thicker soup, simmer uncovered for a few extra minutes after adding the cheese sauce or mash some of the potatoes.
Garnish Ideas: Top with crispy bacon, green onions, extra shredded cheese, or brioche hamburger bun croutons for added texture and taste.
Brioche Croutons: Make them by cutting brioche buns into small cubes, tossing with melted butter and a pinch of salt, and baking at 375°F for 10-12 minutes until golden and crispy. Let cool before adding to the soup.
Slow Cooker Option: Brown the ground beef first, then add it to the slow cooker with onions, carrots, celery, potatoes, broth, salt, basil, and pepper. Cook on low for 6-7 hours or on high for 3-4 hours until the potatoes are tender. Stir in the cheese sauce and sour cream just before serving.