Preheat oven to 375°. Butter an 8x8-inch glass baking dish, and set aside. Melt 3 tablespoons butter over medium heat in a 3- to 4-quart saucepan until bubbling. Add corn and shallot; toss with butter to coat. Add salt and paprika and stir to combine. Cook corn until a few kernels start to brown, about 7 to 10 minutes. Reduce heat to medium-low. Add flour and stir two minutes. Stir in half-and-half and continue cooking, stirring regularly, to create a loose bechamel sauce, about 5 minutes. Check seasoning and add more salt to taste.

Pour into the buttered dish, sprinkle with white or cayenne pepper, if you like, and bake uncovered until lightly browned and bubbly, about 20 minutes.