Place chopped bacon in a large Dutch oven. Cook over medium heat, stirring occasionally, until crispy and cooked through, about 5 minutes. Using a slotted spoon, transfer the bacon to a paper towel–lined plate. Do not wipe the pot clean.
Add cubed potatoes, chopped onion and chopped celery to the drippings in the pot. Cook, stirring occasionally, until the onion is translucent, about 3 minutes. Stir in 6 cups cabbage, 1 teaspoon garlic-and-herb seasoning, ½ teaspoon salt and ½ teaspoon pepper. Cook, stirring, until evenly coated, about 1 minute.
Pour in 6 cups broth; bring to a boil over medium-high heat. Reduce heat to maintain a gentle simmer. Cover and cook, undisturbed, until the potatoes are fork-tender, about 10 minutes. Using the back of a spoon, mash some of the potatoes against the side of the pot until the soup thickens to your desired consistency. Remove from heat. Add ½ cup cream; stir until combined.
Divide the soup evenly among 8 bowls. Top each serving with 2 tablespoons shredded Cheddar, 1 tablespoon cooked bacon, 1½ teaspoons sour cream and 1½ teaspoons chopped chives.
