Cook the lasagna sheets briefly in plenty of boiling, salted water, slowly putting them into the pan vertically one by one (and only a few at a time). After 1 or 2 minutes, use a slotted spoon to remove the sheets from the pan, put them straight into cold water and then strain them again. Spread the lasagne out to dry on a cotton tea towel, one beside the other. Heat the oil and garlic in a heavy-bottomed frying pan. When the garlic has browned, remove it and add the mushrooms, which you have previously cleaned thoroughly with a damp cotton cloth. Cook for 15 minutes, stirring frequently; then turn up the heat to allow any remaining liquid to evaporate, remove from the stove and leave to cool. Now transfer the mushrooms onto a chopping board and chop them coarsely. Put them in a bowl with the ricotta and half of the grated pecorino, season with salt and pepper, stir well to amalgamate everything... and the filling is ready! Place 2 spoonfuls of it in the centre of each lasagna sheet and roll them up to form cannelloni. Mix the béchamel with the ragu in a bowl. Spread 2 or 3 spoonfuls of this mixture in the bottom of an oven dish, arrange the cannelloni in it, one beside the other, and cover them with the remaining sauce. Sprinkle with a handful of grated pecorino, add a few knobs of butter here and there on the surface, and bake in a preheated oven, at 180 °C, for 20-25 minutes.