Peel the potatoes and cut them into pieces, wash the fava beans and put them on the fire in a saucepan together with the potatoes covered with water. As soon as the water boils, remove them from the heat and drain them. Rinse in cold water to remove the foam, drain again and put more cold water, just to barely cover the beans and potatoes. Add a pinch of coarse salt, a small clean garlic, the chopped onion, and the bay leaf. Cover the saucepan and cook over very low heat until the water is completely consumed.
Clean the chicory by cutting off the part in contact with the ground and the bad leaves. Each chicory leaf should be cut in half, and then rinsed thoroughly in running water. Boil the water with the salt and cook the chicory. The cooking time of the chicory depends a lot on the vegetables. Tender and thin seedlings can cook in 10 minutes, larger plants can even take 30-40 minutes, so taste them and remove them from the heat when they seem quite soft and cooked.
From the saucepan with the beans remove the bay leaf and using a potato masher or a mixer, pound everything until you get a puree without lumps. At this point add plenty of olive oil to the puree, and with a wooden spoon mix everything well, first slowly so as not to splash the oil and then faster and faster, until the puree has become well creamy and uniform.
At this point you can drain the chicory from the boiling water. Arrange them on the bottom of the plate, and lay a few spoonfuls of mashed beans on top. Add a drizzle of olive oil to the chicory and mashed potatoes for seasoning.