Peel and devein the shrimp if necessary. Heat 1 tablespoon of butter in a skillet over medium heat. Add shrimp and cook until pink and opaque, about 2-3 minutes. Remove from heat and set aside.

In the same skillet, add the remaining tablespoon of butter. Sauté the chopped onion and celery over medium heat until vegetables are soft, about 5 minutes.

Add diced potatoes and corn kernels, stirring well. Sauté for about 2-3 minutes.

Pour in chicken broth and add the bay leaf, bringing to a gentle simmer. Cover and cook until potatoes are tender, approximately 15-20 minutes.

Stir in half-and-half, and simmer for another 5-10 minutes.

Add the cooked shrimp back into the pot. Simmer for an additional 5 minutes. Adjust seasoning with salt and pepper.

Ladle the chowder into bowls, garnishing with fresh parsley. Serve hot with lemon wedges.