For the shrimp croquettes: Melt the butter in a medium skillet over medium-high heat. Add the shallot and saute until softened, about 4 minutes. Use a wire whisk to stir in the flour. Cook for 1 minute, and then add the shrimp. Stir in the milk and cook until the mixture is very thick, stirring constantly for 1 minute. Remove from the heat and add the lemon juice and some salt and pepper.
Allow the croquette mixture to cool completely before shaping into small meatball-sized balls. Place the breadcrumbs in a shallow dish. Mix the beaten eggs with 2 tablespoons water. Double coat the croquettes by rolling them first in the crumbs, then in the egg mixture, and then in the crumbs again. Place each coated croquette on a baking sheet. Cover the croquettes and set them aside.
For the creamed green peas: Melt the butter in a medium saucepan over medium heat. Stir in the flour and cook until smooth and lightly browned, about 1 minute. Slowly whisk in the milk and continue cooking on medium heat, stirring often. Season with salt and pepper. Cook until the mixture is smooth and thick, about 6 minutes. Stir in the peas, and keep warm while you fry the croquettes.
Heat the oil to about 375 degrees F in a deep, heavy pot. Preheat the oven to 150 degrees F.
Add the croquettes to the hot oil in batches, making sure not to crowd the pan. Cook until golden brown, about 3 minutes. Drain the croquettes on paper towels, sprinkle with salt, and keep warm in the oven as you fry the remaining croquettes. Make sure the oil returns to 375 degrees F before cooking the next batch, or they will be heavy and greasy.
Adapted from "Georgia Cooking in an Oklahoma Kitchen" by Trisha Yearwood © Clarkson Potter 2008. Provided courtesy of Trisha Yearwood. All rights reserved.