For the pastry: pile the flour up on a pastry board, or your work surface and create a “well” in it; put 2 spoonfuls of olive oil in the centre, with the salt and a little water. Gradually incorporate the flour, from the edge towards the centre, using a fork and adding the water a little at a time. When the dough takes shape, continue with your hands until you form a smooth ball. It should be neither too soft, nor too hard. Set aside ¼ of the dough; divide the other ¾ into 5 equal parts and roll them out, using a rolling pin and a little flour to help avoid the pastry sticking to the work surface. Grease a round tart tin (diameter 26 cm) with 1 spoonful of olive oil, and lay the first sheet of pastry in it, making sure it adheres well to the bottom and around the side. Brush the surface with oil, then lay another sheet of pastry on top, brush it with oil and continue in the same way until you have used all the sheets. Now prick all the layers with a fork.
For the filling: in a large bowl, mix the ricotta with the Pesto, add the grated pecorino and the eggs, and amalgamate everything until you have a smooth cream. Pour it onto the pastry base and level the surface with the back of a spoon. Roll out the part of dough you set aside earlier, cut it into strips about 2 cm wide and arrange them in a “lattice” (as you would for a sweet tart) on top of the pesto and ricotta mixture.
Bake in a preheated – fan – oven, at 180 °C, for about 35 minutes, until the pastry has turned a nice golden colour. Leave to cool down before removing the tart from the tin and serving.