Prepare the shrimp by peeling and deveining them. Melt 2 tablespoons of butter in a large pot over medium heat. Add the shrimp, cooking for 2-3 minutes until pink and opaque. Set aside.

In the same pot, add another tablespoon of butter, and sauté the finely chopped onion and celery over medium heat for 5 minutes. Add the diced potatoes and corn, and stir for 2 minutes.

Pour in 4 cups of chicken broth and add a bay leaf. Bring to a gentle boil, then reduce heat to low, cover, and let it simmer for 15-20 minutes until potatoes are tender.

Stir in 1 cup of half-and-half, simmering for another 5-10 minutes over low heat until it thickens slightly, ensuring not to boil.

Return the cooked shrimp to the pot, warming through for 2-3 minutes. Adjust seasoning with salt, pepper, and smoked paprika to taste.

Remove the bay leaf, ladle chowder into bowls, and garnish with parsley. Optionally serve with lemon wedges.