In a large bowl, cover chickpeas with 6 cups (1.4L) cold water. Let stand at room temperature for at least 8 hours or overnight. Drain and rinse chickpeas thoroughly.

In a 6- to 8-quart Dutch oven or saucepan, combine chickpeas and cumin. Add enough water to cover by 2 inches (about 8 cups; about 1.9L) and bring to a boil over high heat. Reduce to a simmer, cover with lid slightly ajar, and cook until chickpeas are completely tender but not falling apart, 1 hour 15 minutes to 1 hour 30 minutes.

Meanwhile, adjust oven rack to middle position and preheat to 350ºF (175ºC). Place sliced pita on a rimmed baking sheet and transfer to oven. Toast, using a spoon or spatula to turn pita occasionally, until squares are completely dry and crisp and starting to darken in color, about 15 minutes. Remove and set aside until ready to use.

In a medium bowl, stir tahini, garlic, salt, yogurt, and lemon juice together until smooth; the sauce should be thick and sticky. When chickpeas are done, add ½ cup to ¾ cup of chickpea cooking liquid to bowl with tahini mixture and whisk well to incorporate.

In a small bowl, combine garlic, green chile, lemon juice, and extra-virgin olive oil for the lemon dressing. Whisk well to combine and season to taste with salt. Set aside.

In a 10-inch skillet, heat olive oil and butter over medium heat until butter has melted. Add pine nuts and toast until light golden brown and fragrant, about 1 ½ minutes. Using a fine-mesh sieve, immediately strain nuts over a small bowl and transfer to a paper-towel lined plate. Set aside.

Return fat to pan. Increase heat to medium-high and add lamb or beef and season with spices and salt. Cook, stirring occasionally until meat is nicely browned and cooked through, about 4 minutes. Season to taste with salt.

To assemble, arrange toasted pita on a large, deep serving platter and spoon half of the lemon dressing on top of the pita. Using a ladle, scoop chickpeas, along with about ½ cup of their cooking liquid, over the bread, reserving 2 tablespoons of chickpeas to garnish with.

Pour the tahini and yogurt mixture evenly over the chickpeas. Top with the fried meat and pine nuts. Garnish with the reserved chickpeas, chopped parsley, and pomegranate seeds, if using. Drizzle the remaining lemon dressing over and top with more olive oil if desired. Serve warm.