1. Bring the water to a rolling boil in a covered saucepan. Add the dry fava beans, reduce the heat and cover. Let the mixture simmer slowly until the fava beans are very soft and falling apart and the water is reduced, about 20 minutes.
2. Once the beans are soft enough to fall apart when you touch them with a wooden spoon, add the salt, pepper, sugar and olive oil to the pan and stir until combined.
3. Place a large, fine wire strainer over another pan or large bowl. Pour some of the pasty bean mixture into the strainer and press it through using a wooden spoon. Repeat until you’ve pressed through all the mixture. Don’t forget to remove the extra from the bottom of the strainer.
You should have a thick, pasty but smooth mixture with no lumps. If your paste seems to thick and dry, stir in about 1 tablespoon more olive oil.
While the paste is still warm, spoon it into a shallow rectangular, square or circle-shaped serving dish about 3 inches deep. Glass works best. I like to use a 9-inch round glass oven dish. Smooth the top of the paste with the bottom of a spoon. Set it aside to cool and set.
4. Once it’s cooled down to room temperature, cover it with plastic wrap and refrigerate it for several hours.
5. When you remove it from the refrigerator, the paste should have set and be firm enough to cut. Wet the blade of a sharp knife and cut the fava into squares or diamonds. Make sure to re-wet the blade often to prevent sticking.
6. Remove the blocks of fava gently and arrange them on your serving plate. Drizzle them with a little extra-virgin olive oil and sprinkle the chopped, fresh dill weed over the top.