1 Melt the butter and oil together in a saucepan over a medium heat. Add the onion and season with salt and pepper. Cook for 4-5 minutes, stirring occasionally, until the onion is soft and translucent.
2 Add the flour and cook for one minute, stirring constantly. Add the milk and cook for 3-4 minutes, whisking constantly. Whisk in the Serrano ham and 40g of the Manchego. Season to taste and remove from the heat.
3 Transfer the mixture to a bowl and allow to cool, then place in the fridge for at least one hour, or up to two days.
4 Beat the eggs in one shallow dish, and stir together the breadcrumbs and remaining Manchego in a second.
5 Scoop heaped tablespoons of the cooled filling, using floured hands to form 5cm croquettes.
6 Working with one croquette at a time, coat them in the beaten egg, then dredge in the breadcrumbs, gently pressing them on to coat. Transfer to a baking tray lined with parchment paper.
7 Heat 5cm of vegetable oil in a large, heavy pot until it registers 190˚C on a thermometer, or until a breadcrumb dropped into the oil sizzles on impact.
8 Working in small batches to avoid crowding the pan, deep-fry the croquettes for 1-2 minutes until deep golden brown, flipping once halfway through. Using a slotted spoon, transfer to a plate lined with kitchen paper to drain. Serve immediately.