Over medium heat, cook the chopped bacon until it's almost crisp.
Add the onion, celery, carrot, and potato to the bacon. Stir and cook for about 2 minutes.
Pour the juice from the clams over the veggies and bacon.
Add the stock and the seasonings to the pot, and boil gently until the potatoes are tender.
Whisk the flour into 2 cups of half and half. Add to the pot, and stir until the liquid thickens.
Stir in the remaining half and half, add the clams, and bring to a simmer.