In a large Dutch oven or heavy-bottomed pot, cook the chopped bacon over medium heat until crispy (about 6-8 minutes). Use a slotted spoon to remove the bacon to a paper towel-lined plate, leaving the flavorful bacon grease in the pot.
Melt the butter in the pot with the bacon grease. Add the diced onion and celery. Sauté for 5 minutes until soft and translucent. Stir in the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the softened vegetables and stir constantly for 1-2 minutes to create a roux (this cooks out the raw flour taste).
Gradually pour in the chicken broth and the reserved clam juice from the cans (keep the actual clam meat aside for now). Whisk continuously until the liquid is smooth and slightly thickened.
Add the diced potatoes and dried thyme to the pot. Bring the soup to a gentle boil, then reduce the heat to low, cover, and simmer for 15 minutes, or until the potatoes are completely fork-tender.
Stir in the heavy cream, milk, and the reserved chopped clams. Season with salt and black pepper. Let the soup simmer gently for 3-5 minutes until heated through. (Do not let it boil vigorously, or the clams will become tough and rubbery).
Stir half of the crispy bacon back into the pot. Ladle the hot chowder into bowls and garnish with the remaining bacon. Serve immediately, preferably with oyster crackers!