Bring a large pot of salted water to a boil. Add the shelled favas, and blanch until bright green and tender, about 5 to 7 minutes, depending on their size. Cool in a bowl of ice water. Peel off the skins and discard. You should have about 2 cups peeled favas.

In a food processor, combine the favas, sesame seeds (reserving 1 tablespoon for garnish), lemon juice, garlic, and salt. With the machine running, add the olive oil in a stream to make a thick, chunky paste. With the machine still running, add warm water, a few tablespoons at a time (up to ⅓ cup), to thin the dip to your liking. It should be about the consistency of hummus.

Transfer the dip to a serving bowl. Garnish with remaining sesame seeds, and serve with flatbread or bread sticks for dipping