In the bowl of a food processor, place the chickpeas. On a cutting board, mash the garlic cloves with 1/4 teaspoon of salt to a smooth paste with the side of a knife, then add this to the processor along with the crushed red pepper, tahini, water, 4 tablespoons of the lemon juice, and 2 tablespoons of the olive oil. Process until smooth, stopping to scrape down the sides as needed. Taste and adjust the seasoning by adding salt and additional lemon juice, if necessary, to taste. Transfer to a wide shallow bowl for serving and use the back of a serving spoon to form a well in the center of the hummus. Set aside.

In a small nonstick skillet over medium high heat, add the meat, allspice, cinnamon, pepper, cumin, and salt to taste and cook, stirring, until meat is browned and the spices are fragrant, about 4 minutes. Drain off any fat, then spoon the beef into the well of the hummus. Drizzle the hummus with the remaining olive oil and sprinkle with the parsley and paprika, to garnish. Serve with pita bread wedges.