Heat 2 teaspoons olive oil in a skillet over medium heat; cook and stir the onion in the hot oil until tender, about 5 minutes. Add the fava beans, garbanzo beans, and water to the onion; bring to a boil, stirring occasionally. Stir the tomato paste, lemon juice, 1 tablespoon olive oil, the garlic, tahini, and cumin through the bean mixture; return the mixture to a boil and allow to cook at a boil for 5 minutes. Remove from heat.
Pour the mixture into a blender. Hold the lid of the blender in place with a towel and start the blender, using a few quick pulses to get the mixture moving before leaving it on to puree to your desired consistency.