Fry the bacon in a deep saucepan until very crispy. Remove and reserve the bacon. Add the onion to the bacon fat and fry until softened. Add the celery, thyme and bay leaves and fry over medium-low heat 5-10 minutes.
Add 2/3 of the milk and the whole corn to the saucepan (if the corn are too large, cut in half). Simmer over low heat 30 minutes, stirring occasionally.
Remove the bay leaves and the corn. Slice off the kernels from the cob and add half the kernels back to the saucepan. Simmer another 5 minutes, then puree with an immersion blender, adding more milk as necessary so the soup is not too thick.
Add the remaining corn to the soup and simmer 5 minutes. Season with salt and pepper and serve, garnished with crumbled bacon.