Béchamel-Coated Crispy Shrimp Delight

Prepare the cooking liquid by simmering the shrimp in their shells until they turn pink, about 2 to 3 minutes.
Transfer the shrimp to a medium bowl, preserving the cooking liquid.
Return the shells to the broth and continue simmering for an additional 15 minutes.
Strain the broth, reserving ¾ cup and discarding the solids.
(Save the remaining broth for enhancing the flavor of future shellfish boils.
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In a medium saucepan over medium heat, melt the butter.
Add the flour and cook, stirring for 1 minute.
Incorporate the reserved broth, milk, lemon juice, salt, and pepper.
Stir continuously until the sauce thickens and becomes smooth.
Allow the sauce to cool, stirring occasionally.
Coat each shrimp generously with the sauce, ensuring full coverage on all sides.
Place the coated shrimp on a dish, cover, and refrigerate for at least 1 hour until the sauce solidifies.
Heat at least ½ inch of oil in a medium skillet over medium-high heat (or use a deep fryer set at 365°F).
Test the oil's readiness by ensuring it turns a cube of bread light brown in 60 seconds.
Prepare two shallow bowls – one with beaten eggs and the other with bread crumbs.
Dip each sauced shrimp in the eggs, coat with bread crumbs, and carefully place in the hot oil.
Fry in batches to avoid overcrowding.
Cook, turning once, until the shrimp achieve a delightful golden brown color, approximately 5 minutes.
Let the fried shrimp drain on paper towels, season with salt and pepper, and serve piping hot.