Heat a large skillet over medium-high heat and add the ground beef. Break it apart and cook 6 to 8 minutes until no pink remains and the meat is well browned.
Add the diced onion during the last 3 minutes and cook until softened. Drain excess grease, then transfer the beef and onion to the slow cooker.
Add the shredded carrots, diced celery, and diced potatoes on top of the beef. Pour in the chicken broth and sprinkle in the basil and parsley. Season with salt and pepper, then stir to distribute evenly.
Cover and cook on LOW for 6 to 7 hours or on HIGH for 3 to 4 hours, until the potatoes are fork-tender and the carrots have softened. Avoid lifting the lid repeatedly.
About 30 minutes before serving, melt the butter in a small saucepan over medium heat. Whisk in the flour and cook 1 to 2 minutes until nutty and pale gold.
Slowly pour in the milk while whisking and keep whisking until the mixture thickens into a smooth, pourable sauce, about 4 to 5 minutes.
Pour the thickened milk mixture into the slow cooker and stir it through the soup. Add the shredded cheddar a handful at a time, stirring after each addition until fully melted.
Cover and cook on LOW for another 20 to 30 minutes until the soup is thick, creamy, and heated through.
Taste and adjust with more salt and pepper as needed. If too thick, stir in a splash of warm broth or milk to loosen it.
Ladle into bowls and finish with crumbled bacon, green onions, extra cheddar, or a few dill pickle chips for that true cheeseburger touch.