Melt 2 tablespoons butter in a medium Dutch oven over medium heat. Add the bacon and cook, stirring occasionally, until crisp, about 6 minutes. Transfer to paper towels to drain.
Drain or spoon off all but 3 tablespoons of the fat in the pot. Add the onion, bell pepper and celery and cook, stirring occasionally, until the vegetables just begin to become tender, about 5 minutes. Season with salt and pepper and add the flour, thyme and bay leaves. Stir the flour into the vegetables to make a paste and coat them evenly. Cook a minute or two to get rid of the raw flour flavor. Add the chicken broth and bring to a simmer. Cover and cook until the vegetables are tender, 15 minutes.
Uncover the pot and add the potato, half-and-half and all but 1/2 cup of the corn. Simmer, uncovered, until the potato is very tender but not yet falling apart, 10 to 12 minutes.
Meanwhile, melt the remaining 1 tablespoon butter in a medium skillet over medium-high heat. Add the reserved ½ cup corn and cook, stirring, until warmed through, 6 to 8 minutes.
Discard the bay leaves from the soup. Puree about 1 cup of the soup in a food processor or blender and stir it back into the soup. Ladle the soup into bowls and garnish with the cooked bacon and buttered corn kernels.