Pile the semolina flour up on your work surface and create a “well” in the centre. Break the eggs into it, add the red pesto and gradually pour in the water, slowly mixing everything together with a fork, and using the flour from around the edge, a little at a time, as you continue mixing. When the dough has become fairly compact, knead it with your hands and finish incorporating all the flour. Continue for 10-15 minutes until you have a smooth, elastic dough, which you will then leave to rest for half an hour covered with a cotton cloth. When this time has passed, divide the dough in half and roll out one part with a rolling pin, or with a pasta-making machine, until you have a thin sheet, always using a little flour so that it doesn’t stick to anything, and trying to give the sheet of pasta an oval shape. Fold the first sheet over on top of itself several times starting from the two longer edges, and the cut it into strips about 2 cm wide using a sharp knife. Sprinkle with a little flour, open the strips out with your hands to form small “nests” and arrange them on a cotton tea towel. Repeat with the other half of the dough.
Now prepare the sauce. Heat 3 spoonfuls of olive oil in a heavy-bottomed frying pan, add the well drained tuna, the olives, capers (previously rinsed under running water), fennel seeds, chopped basil and thyme leaves, and grated lemon peel. Cook over a lively heat for about 10 minutes. Turn the heat off and sprinkle with oregano.
Cook the pappardelle in plenty of boiling salted water, use a slotted spoon to strain them when “al dente” (setting aside a cup of their cooking water) and toss them delicately in the pan with the sauce for a couple of minutes. If you see that the pasta is becoming too dry, add a ladle of its cooking water. Sprinkle with crumbled Taralli and coarsely chopped almonds, then serve immediately while still nice and hot!