Make the lemon-y tahini. In a medium bowl, whisk together the tahini, water, lemon zest, lemon juice, garlic, olive oil, salt, and pepper. Once combined and seasoned to your liking, set aside.
Preheat the oven to 400°F. Cut the potatoes into 1-inch thick wedges or cubes and transfer them to a large baking sheet. Toss them with the oil, za’atar, salt, and pepper. Place potatoes in the oven and roast for about 40 minutes, or until tender and golden brown, flipping them once at the halfway point.
Make the harissa chickpeas. In a deep skillet over medium heat, toast the cumin, coriander, caraway, and chili flakes until fragrant, about 1 minute. Transfer spiced to a spice grinder or mortar and pestle. Grind spices to a rough powder and set aside.
Place the skillet back on the heat and pour the oil in. Add the shallot to the skillet and sauté until translucent and soft, about 3 minutes. Add the garlic and ground spice mixture and stir until fragrant, about 30 seconds. Add the chickpeas to skillet and stir to coat the chickpeas. Add the crushed tomatoes and water to the chickpeas and stir to combine. Season harissa chickpeas with salt and pepper. Bring the harissa chickpeas to a boil. Lower heat to a simmer and let chickpeas cook for 10 minutes, adding more water if necessary. You want the chickpeas to be saucy, but not fluid like a soup.
While chickpeas are simmering, toss the greens with olive oil, lemon juice, pinches of za’atar, sale, and pepper.
To serve the harissa chickpea bowls, divide warm potatoes among plates. Top with harissa chickpeas, tahini sauce, piles of dressed greens, and chopped parsley.