For the pasta dough, put the flour, salt and egg yolks in the bowl of a food processor. Pulse until the mixture begins to resemble fine breadcrumbs.
Remove the dough from the bowl and knead to form into a ball. With the heel of your hand, knead it four or five times, then wrap in cling film and refrigerate for at least 30 minutes.
Using a pasta machine, roll the dough, starting on the widest setting and roll it through repeatedly, narrowing the setting by one notch each time, until the sheet of dough is 1.5 mm thick.
On half the sheet, spread and scatter the small basil leaves. Fold the plain half over to cover them. Press down gently with the palms of your hands.
Roll the dough back to 1.5 mm thick then cut into four rectangles 8x15cm/3x6in.
Cook in gently simmering salted water with the olive oil for approximately 3-4 minutes.
Refresh in cold water, drain and place the sheets flat on a tray and cover with cling film. Reserve in the fridge.
For the crab filling crush the peppercorns with the side of the blade of a chopping knife. Put them in a bowl, add the crab, the olive oil, the lime juice and season to taste.
For crab coral purée, pass the coral through a fine sieve. Add the mascarpone, whisk together, season and warm through just before serving.
For virgin olive oil sauce, peel, deseed and cut the tomatoes into small diamond shapes and place in a saucepan with all the other ingredients. Mix gently and season to taste. Warm the sauce slightly just before serving.
To serve, garnish each cooked rectangular sheet of pasta with the crab filling. Roll tightly and reheat in a steamer for 3-4 minutes. Cook the asparagus slices at the same time in the steamer.
In a warm plate, spoon on some crab coral purée (if using). Place on top a warm cannelloni.
Pour the sauce over and around then garnish with the asparagus slices and rocket leaves and serve.