1. Bring 5 cups water, the fava beans, whole garlic cloves, and 1/2 teaspoon salt to a boil in a medium saucepan. Reduce heat, and simmer until beans are tender, about 30 minutes. Drain well; let stand until cool, about 15 minutes.

2. Crumble sausage into a large skillet. Cook over medium heat, stirring and draining off fat occasionally, 6 minutes. Add sliced garlic. Cook, stirring occasionally, until sausage is cooked through and garlic is crisp, about 4 minutes more.

3. Put bean mixture, oil, tahini, lemon juice and zest, 3/4 teaspoon salt, a pinch of pepper, and 1/4 cup water in a food processor. Process, adding up to 1/4 cup more water, until smooth and creamy. Season with salt and pepper.

4. Smooth dip in an even layer on a platter. Using a slotted spoon, arrange sausage on top. Top with parsley; drizzle with oil. Serve with flatbread crisps.