Warm the milk in a microwave-safe jug for 2 to 3 minutes until steaming but not boiling. Melt the butter in a 3-quart / 2.8 L (20 cm / 8-inch) heavy saucepan over medium-low heat, add the onion, and cook for 5 minutes until soft and translucent but not browned.

Stir in the diced jamón serrano and cook for 1 minute. Add the 80 g flour all at once and stir for 2 minutes until the paste smells toasty and looks pale blond.

Pour in the warm milk about 120 ml / 1/2 cup at a time, whisking until smooth before adding more. Switch to a wooden spoon and cook over medium-low heat for 8 to 10 minutes, stirring constantly and scraping the corners, until the mixture pulls away from the sides of the pan in one mass. Stir in the nutmeg and pepper, then taste and add salt only if needed.

Spread the béchamel in a 20 x 30 cm / 8 x 12 inch shallow dish and press plastic wrap directly onto the surface. Cool for 20 minutes on the counter, then refrigerate until cold and firm, at least 4 hours in total or up to 24 hours.

Set out three shallow bowls with the 40 g flour, the beaten eggs, and the breadcrumbs, plus a lined tray. Scoop about 2 tbsp / 30 g of cold béchamel and roll it between floured palms into a log about 6 cm / 2.5 inches long. Coat in flour and tap off the excess, then dip in egg, roll in crumbs, dip in egg again, and roll in crumbs a second time, pressing the ends closed. Place on the tray. You will have about 28.

Pour the oil into a 26 cm / 10-inch (5-quart / 4.7 L) Dutch oven to a depth of about 5 cm / 2 inches and heat to 180 C / 355 F, about 8 minutes. Fry 7 croquetas at a time for 2 to 3 minutes, turning once, until deep golden brown all over. Lift out with a slotted spoon onto a paper towel-lined tray, let the oil return to 180 C / 355 F, and repeat for 4 batches in total. Serve within 10 minutes.