Mix flour and eggs until a sticky dough forms.
Knead the dough on a floured surface until smooth.
Chill the wrapped dough in the fridge for 20 minutes.
Flatten three equal dough pieces to 1cm thickness.
Roll dough through the widest setting of a floured pasta machine.
Repeat rolling at progressively thinner settings until the penultimate setting is reached.
Cut the pasta sheets into 3mm thick linguine strips.
Dry the pasta on a rack while preparing the sauce.
Fry onions and garlic in oil until softened.
Add carrot, celery, and bacon and fry for several minutes.
Brown the beef mince in the pan.
Stir in tomato purée, tinned tomatoes, and red wine and boil.
Simmer with half the basil for 45 minutes until thickened.
Boil the pasta for 3-4 minutes until tender.
Drain pasta and toss with the ragu and remaining basil.
Serve topped with grated Parmesan.