To make the béchamel, warm the milk in a pan over a low heat. Put the butter into a separate pan and let it melt on a low heat. When the butter is melted (don’t let it colour), add the flour and mix together well, then cook for 1 minute. Add the warmed milk: start with a quarter of it at first, stirring continuously, then add another quarter and keep stirring. Continue cooking and stirring until you’ve used up all the milk. Adding it little by little keeps the béchamel thick and creamy. You need to cook béchamel for 20 minutes to cook off the flour. Season, mix in the grated nutmeg and chopped honey ham, then remove from the heat.
Whisk 2 of the eggs in a bowl and set aside. Boil the rest of the eggs for 7 minutes in boiling water. Peel under cold running water, then cut them in half. Carefully remove the yolks, then chop them and add to the béchamel, mixing together to incorporate. Once the béchamel mixture is cool, spoon it into the egg halves to fill them. Cover the filled eggs and leave in the fridge until set. When the eggs are set, remove and dip completely first into the whisked egg, then into the flour. Heat the oil in a high-sided pan on a medium heat and shallow-fry the eggs until golden and crispy.
Place the eggs on slices of bread to make pintxos. Dust with salt and pepper and a little smoked paprika.