First make the pasta. Put the flour into a large bowl, then make a well in the centre. Add the eggs, olive oil and salt to the well and whisk together, then gradually stir in the flour, pulling a little flour in each time you stir the mixture to make a smooth, firm dough.
Flatten the dough into a disc about 1cm thick, then wrap in clingfilm and chill in the fridge for 20 minutes.
Unwrap the chilled dough and lay it on a lightly floured work surface, then cut it in half. Roll out each portion of dough to a rectangle about 5mm thick, turning it as you go to ensure you have an even thickness, then roll each portion again to about 2mm thick – the thinner the better. When the pasta is as thin as you can go, cut it into strips about 3mm wide for tagliatelle or thinner for linguine.
Hang the pasta strips over a clean broom handle or rolling pin to allow them to dry slightly while you cook the broccoli for the sauce.
Bring a saucepan of water to the boil, then add the broccoli and cook for 4–5 minutes until just tender. Drain well, set aside and keep warm.
Bring a separate large saucepan of salted water to the boil. Add the pasta, return to the boil and cook for 3–4 minutes until it rises to the surface. Drain into a colander, reserving some of the cooking water, then return the pasta to the pan.
Add the broccoli, anchovies and olive oil to the pasta and toss well to combine. Add about 2 tablespoons of the reserved pasta water and cook for 1 minute, stirring as you go. The pasta should be evenly coated in the sauce.
Season to taste, then pile the pasta into serving bowls, sprinkle over the Parmesan and serve immediately.