Put the flour, olive oil and eggs in a food mixer or food processor and blend until the ingredients come together and form a dough. Keep mixing for a minute, removing the lid and turning the dough every 15-20 seconds. This will help make the dough smoother. Take care to avoid cutting your fingers on the blade if using a food processor.
Alternatively, bring the ingredients together with your hands, working the eggs into the flour a little at a time.
Turn the dough out onto a lightly floured surface and knead hard for 10 minutes, really pummelling and stretching the dough until it is silky with a slight sheen. Wrap in cling film and chill in the fridge for 30 minutes. Line a couple of large trays with baking parchment and sprinkle with a little sifted flour (these will be used to lay out the fresh pasta to dry).
Take the pasta from the fridge and remove the cling film. Divide into three pieces and rewrap two of them. Form the remaining pasta into a block and roll out on a very lightly floured surface as thinly as you can – even thinner than a two pence piece. You want to end up with a rectangle roughly 48x30cm/19x12in. Turn the dough regularly and sprinkle with a tiny amount of flour if it begins to stick. Don’t worry if it isn’t perfect, as long as you can make some good, wide strips, no-one will notice.
Cut the pasta into wide strips – you’ll need to make them roughly 2.5cm/1in wide and around 30cm/12in long. Arrange the strips on the trays, keeping each strand a few millimetres from the next. Repeat exactly the same process with the remaining pasta.
The pasta can be left to dry for a few hours at this point or used immediately. If your trays get too full, cover with another layer of baking parchment and a sprinkling of flour then create another layer. (You can also hang the pasta on a broom handle wrapped in cling film and suspended between two chairs.)
When you are ready to cook the pasta, half-fill a very large saucepan with cold water, add the fine sea salt and bring to the boil. Drop the pasta gently into the hot water and return to the boil, swishing around with a long wooden spoon to separate the strands.
Cook for 2-3 minutes, or until the pasta is tender but firm, stirring occasionally. You can test the pasta by removing one of the pieces and cutting a little off one end to taste. (If your pan isn’t large enough for all the pasta, cook in two batches, tossing the first batch with a little olive oil once it has been drained.)
Drain the pasta in a colander and return to the saucepan. Toss with a little olive oil and seasoning or the pasta sauce of your choice. Tip into a warmed serving dish and serve immediately.