Cook bacon in a large dutch oven over medium heat until crisp. Remove with a slotted spoon and transfer to a paper towel lined plate.
Add chopped onion, sliced carrots, and sliced celery to the bacon grease in the pan. Sauté vegetables until crisp tender, about 10 minutes, stirring frequently.
Add minced garlic to the pot and cook until fragrant, about 1 minute.
Add flour to the pan and cook for 3-4 minutes, stirring constantly until lightly toasted.
Add diced potatoes, chicken broth, salt, pepper, thyme and bay leaf to the pot.
Increase heat and bring to a boil. Cook until potatoes are soft but not falling apart, about 15 minutes.
Fish out bay leaf and discard.
Stir in milk stirring constantly. Bring to a simmer stirring occasionally and cook until soup thickens, about 15 minutes.
Stir in half the shedded cheddar cheese and half the bacon. Stir until cheese is melted into the soup.
To serve, top each bowl with some shredded cheese, crumbled bacon and garnish with chives.