Heat the olive oil in a thick-bottomed saucepan. Add two-thirds of the prosciutto and fry for one minute.
Add 50g/2oz of the butter to the pan and allow to melt, then add the wine and simmer for 2-3 minutes, just to combine with the butter and the prosciutto juices.
Place the egg yolks, parmesan and pecorino into a bowl and season, to taste, with salt and freshly ground black pepper.
Cook the tagliatelle according to the packet instructions, or until al dente, then drain, reserving a few tablespoons of the cooking water.
Immediately add the pasta to the prosciutto mixture, then stir in the egg mixture - the heat of the pasta will cook the egg.
Add the reserved cooking water if the sauce seems too thick, then stir in the remaining prosciutto and reserved butter.
To serve, spoon into warmed bowls and sprinkle with a little extra parmesan.