First of all clean the artichokes: use a sharp knife to cut off the stalk, leaving a piece roughly 5 cm long. Remove the outermost petals by hand, cut off the “tip” of the artichoke and then the tough extremity of the remaining petals, leaving just the tender part and the inside, the “heart” of the artichoke. As you prepare the artichokes, put them in a bowl full of water, with the juice of the lemon and the two squeezed halves of the fruit. Let them soak for 10-15 minutes, then strain and pat them dry with kitchen paper. In a heavy-bottomed frying pan, lightly sauté the cloves of garlic in the olive oil. Now put the thinly sliced artichokes into the pan as well. Season with salt and pepper and stir; when the artichokes begin to brown, pour in ½ a glass of water so they can finish cooking without drying out too much. Remove the garlic and set the artichokes aside.
Now prepare the béchamel: put the butter in a small (heavy-bottomed) pan over a low heat. As soon as it has melted, add the flour and stir for 2-3 minutes with a wooden spoon, without letting the mixture brown. In the meanwhile bring the milk to the boil. Pour a small amount of boiling milk into the saucepan and mix thoroughly; gradually add all the milk, stirring constantly. Cook for approximately 10 minutes, over a very low heat, stirring continuously and taking care that the sauce doesn’t stick to the bottom of the pan. Turn the heat off and season with salt and nutmeg. Put the béchamel to one side and, to avoid a “skin” forming on top, cover with cling film in contact with the surface.
Take the saucepan with the artichokes; set 2 large spoonfuls of them aside in a bowl and then, using a knife, coarsely chop the rest on a chopping board. Stir the grated cheese and chopped artichokes into the béchamel. Pour a ladle of this mixture into the bottom of an oven dish (1) and spread it out well; cover with a layer of lasagna, placing the sheets of pasta one beside the other and covering the entire surface. Add some more “sauce” (the béchamel and artichoke mixture), then another layer of lasagna, and continue in this way until you have used all the ingredients, finishing with the “sauce”. Distribute the artichoke slices you set aside and the knobs of butter on top, and sprinkle with a few spoonfuls of grated cheese. Bake in a preheated oven, at 180 °C, for 15 minutes.
(1) You can also prepare the lasagna in individual portions, using small single-serving ramekins.