Drain the juice from clams into a large pot; set the clams aside. Add the celery, onions, and potatoes to the pot, and add just enough water to cover the vegetables. Cover the pot with a lid, and cook over medium heat until the potatoes are tender, about 15 minutes.
Meanwhile, in a small saucepan, warm the half-and-half, stirring occasionally; do not boil.
In a medium saucepan, melt the butter over medium heat. Whisk in flour until smooth. Slowly whisk in half-and-half, stirring constantly, until thick and smooth, about 5 minutes.
Carefully, pour the cream sauce into the vegetable pot, along with the clams, stir to combine. Season with salt, pepper, and thyme.
Using a serrated knife, cut the top off of the sourdough bread. Hollow out to make a bowl, leaving a 1-inch wall and bottom. Reserve the bread pieces for dipping. Ladle chowder into bowls and serve with bread pieces.