In a large pot over medium heat, cook the bacon until crisp, about 5 minutes.
Add the butter and melt.
Stir in the onion and carrot; sauté for 5 minutes.
Add the leek and potatoes; continue sautéing for 2 to 3 minutes more. Season with salt and pepper.
Once the onions and leeks have softened and become slightly translucent, add the thyme and corn; stir to combine.
Sprinkle the flour over the vegetable mixture and stir well to form a thick roux, about 3 minutes.
While whisking, pour in the clam juice in a steady stream until fully incorporated and no lumps remain. Reduce heat to medium-low and simmer for about 8 minutes, or until the mixture thickens, stirring frequently to prevent burning on the bottom.
Stir in the clams and milk; continue to simmer for an additional 12 to 16 minutes, stirring frequently.
Adjust seasonings and serve hot, in hollowed-out sourdough bread bowls if desired.