Begin by making the hummus: Rinse the chickpeas and then place them in a three quart saucepan. Fill the pot with water and bring it to a boil over high heat. Boil for ten minutes and then take it off the flame and let it sit for one hour. Drain and rinse the beans.
Put the beans back in the pot and cover with water. Simmer the beans until they're tender, for about 90 minutes. You may need to add additional water.
While the beans cook, roast the sweet potatoes: Preheat the oven to 425 degrees. Place the potatoes on a sheet pan and roast them for 90 minutes. Remove the skins and scoop out two cups of the flesh.
Drain the beans and put them in the food processor. Add the garlic, oil, tahini, sweet potatoes, water, lemon juice and salt. Process the ingredients until it's all smooth and fluffy.
Brush the pitas with some olive oil and grill them until they're toasted on both sides.
Serve the hummus with the pita bread, peppers, and cherry tomatoes.