Place half the chickpeas and half the cannelloni beans in the bowl of a food processor along with garlic and yogurt. Puree until smooth. Add remaining beans, and pulse until coarsely chopped.
Set aside 2 tablespoons tomato for garnish. Transfer mixture to a bowl; stir in remaining tomato, cumin, 1/2 teaspoon salt, 1/4 teaspoon pepper, and lemon juice. Set aside.
Heat a grill or grill pan over medium-high heat. In a small bowl, combine remaining teaspoon salt, 1/4 teaspoon pepper, thyme, and parsley. Spray both sides of pitas with cooking spray, and place on grill. When bottoms are browned, about 30 seconds, flip pitas, and sprinkle one of the cooked sides with herb mixture. Cook until both sides are browned. Cut pitas into wedges; serve warm with reserved bean dip. Garnish with reserved chopped tomato.