Melt the unsalted butter in a medium saucepan over medium heat. Add the finely minced Serrano ham and sauté for 1 to 2 minutes until fragrant and slightly crisped.

Sprinkle 1/2 cup of all-purpose flour into the saucepan with the ham. Stir constantly with a wooden spoon for about 2 minutes to cook out the raw flour taste, creating a smooth roux.

Slowly pour in the warm whole milk in a steady stream, whisking vigorously to prevent any lumps from forming. Cook, stirring constantly, until the béchamel thickens into a very thick paste that cleanly pulls away from the sides of the pan, about 5 to 7 minutes.

Stir in the ground nutmeg, salt, and black pepper. Transfer the smooth croqueta mixture to a shallow baking dish, press plastic wrap directly onto the surface of the dough to prevent a skin from forming, and refrigerate for at least 2 hours until completely firm.

Once the mixture is chilled and firm, scoop tablespoon-sized portions and roll them between your hands into small cylinders or log shapes about 2 inches long.

Set up a shallow-bowl breading station: one bowl with the remaining 1/2 cup of flour, a second bowl with the beaten eggs, and a third bowl with the fine breadcrumbs. Coat each croqueta lightly in the flour, dip completely into the egg, and then roll in the breadcrumbs until fully coated.

Heat 2 inches of vegetable oil in a deep frying pan to 350°F (175°C). Fry the croquetas in small batches for 2 to 3 minutes, turning occasionally, until they are beautifully golden brown and crispy all over.

Remove the croquetas with a slotted spoon and drain them on a paper towel-lined plate. Serve immediately while hot and creamy, ideally alongside a fresh garlic aioli dipping sauce and lemon wedges.