Place the fava beans in a pot and cover with water up to 1/2 inch above the fava beans. Salt to taste and let the fava beans soak overnight.
The next day, as some of the water will have been absorbed by the fava beans, add a bit more water to cover the fava beans completely.
Cover the pot and start to cook at very low heat. It is imperative that while the fava beans are cooking you do not stir them until they are completely cooked, otherwise they will stick to the bottom of the pot.
They will cook for about 2 hours. The fava beans will turn into a puree. While they are boiling, if you notice that the water level has lowered, add some boiling water.
After they finished cooking, stir the fava beans with a wooden spoon and add a bit of olive oil.
In a separate large pot, boil water and cook the chicory. Add salt to the water as per your taste.
Cook the chicory for about 10 minutes or to your desired crunchiness.
Drain the water and place in a serving bowl.
Add 1/2 of the fava beans, mix and serve. Add a dash of olive oil on each individual serving.
The other 1/2 of the fava beans should be saved for the next day to make Penne con Fave (see Recipe).