For the pasta, place the flour in a large bowl, make a well in the centre and crack in the egg yolks and whole eggs.
Mix well until the dough comes together as a ball, then knead on a clean work surface, using your hands, for about five minutes.
Cover and leave to rest in the fridge for as long as possible - you can cut the pasta you don't wish to use into portions and freeze any extra for another dish.
Dust a pasta machine with flour starting at the lowest (thickest) setting, feed the dough through the machine, turning the handle with one hand and holding the dough as it comes through the machine with the other.
Change the setting on the pasta machine to the next-thickest setting, flour it again and feed the pasta sheet through the machine again, as before.
Repeat this process 3-4 more times, flouring the machine and changing the setting down each time - it helps to cut the pasta into smaller squares as this will mean the pasta is less likely to dry out (any pasta you are not working on should be covered with cling film).
Finally pass the pasta through the tagliatelle cutter on the machine. Cover and set the pasta aside while you prepare the lamb chops.
For the lamb chops, with a sharp knife, cut a small pocket into the side of each of the lamb chops. Cut a small piece off the end of each slice of ham. Stuff the ham pieces and equal amounts of the quartered sage leaves inside each pocket, reserving the whole sage leaves.
Season the chops with salt and freshly ground black pepper, then cut each piece of ham in half and wrap each chop with ham to cover.
Heat a frying pan until hot, add the butter and the wrapped chops and fry in batches on each side for 3-4 minutes, or until cooked through.
Meanwhile, heat a separate small frying pan until hot, add the oil and heat. Add the reserved whole sage leaves and fry for one minute, or until crisp. Drain the fried sage on kitchen paper.
To cook the pasta, bring a large pan of salted water to the boil and add the pasta. Boil the pasta for 2-3 minutes, then drain and mix it in butter with the chopped sage.
To serve, pile the pasta onto each of four places, place three chops alongside and garnish with the fried sage leaves.
