Heat a large Dutch oven or heavy-bottomed pot over medium heat. Add chopped bacon and cook for 6-8 minutes until crispy and golden. Remove bacon with a slotted spoon and set aside on paper towels. Leave about 2 tablespoons of bacon fat in the pot.

Add diced onion and celery to the bacon fat. Cook for 4-5 minutes until the onion becomes translucent and fragrant. Stir in minced garlic and cook for another 30 seconds until aromatic.

Pour in the chicken broth and add cubed potatoes along with thyme. Bring to a boil, then reduce heat to medium-low and simmer for 18-20 minutes until potatoes are fork-tender but not falling apart.

In a small bowl, whisk flour with 1/2 cup of heavy cream until smooth. Slowly stir this mixture into the soup along with butter and remaining cream. Simmer for 5 more minutes, stirring occasionally.

Using a potato masher, lightly mash about half the potatoes directly in the pot. Season with salt and pepper. Stir in most of the crispy bacon, reserving some for garnish. Serve topped with reserved bacon, cheddar cheese, and sliced green onions.