Melt the butter in a Dutch oven or large pot over medium-high heat. Stir in the celery, scallions, potatoes and corn. Add the thyme, bay leaves, 1/2 teaspoon salt and a few grinds of pepper and cook, stirring, 3 minutes. Stir in the flour until incorporated, about 2 minutes. Stir in the milk, then cover and bring to a boil. Uncover, reduce the heat to medium low and gently simmer until the vegetables are tender, about 6 minutes. Remove from the heat. Discard the thyme sprigs and bay leaves.
Transfer one-third of the mixture to a blender and puree until smooth, then return to the pot. Return to a simmer over medium-high heat. Stir in the shrimp and cook until opaque, about 4 minutes. Season with salt. If the soup is too thick, stir in up to 1 cup water. Divide among bowls and sprinkle with paprika.