Marinate the harissa chicken: In a large mixing bowl, whisk together the harissa paste, olive oil, minced garlic, ground cumin, ground coriander, smoked paprika, honey or maple syrup, lemon juice, salt, and black pepper until smooth. If using chicken breasts, pound them to an even 1/2-inch thickness for even cooking; trim any excess fat from thighs if using. Add the chicken to the bowl and turn to coat well in the marinade. Cover and refrigerate for at least 30 minutes, ideally 2 to 4 hours, or overnight for deeper flavor.
Cook the harissa chicken (grill, skillet, oven, or air fryer): For the grill, preheat to medium-high heat and lightly oil the grates. Grill the chicken for 5 to 7 minutes per side, until the internal temperature reaches 165°F (74°C). For the stovetop, heat 1 tablespoon of olive oil in a large skillet over medium-high heat and cook the chicken for 6 to 8 minutes per side until browned and cooked through. For the oven, preheat to 425°F (220°C), place the chicken on a lined baking sheet, and roast for 18 to 22 minutes, until it reaches 165°F. For the air fryer, preheat to 375°F (190°C), lightly grease the basket, and cook the chicken in a single layer for 10 to 14 minutes, flipping halfway through, until done. Transfer cooked chicken to a cutting board and let rest for 5 minutes, then slice into strips.
Cook the basmati rice: Rinse 1 cup of basmati rice under cold water until the water runs clear. In a medium saucepan, combine the rice with 1 1/2 cups of water and a pinch of salt. Bring to a boil, then reduce the heat to low, cover, and simmer for 15 minutes. Remove from heat and let stand, covered, for 5 minutes. Fluff with a fork and add a squeeze of lemon juice if desired.
Cook the quinoa: Rinse 1 cup of quinoa under cold water. In a medium saucepan, combine the quinoa with 2 cups of water or broth and a pinch of salt. Bring to a boil, then reduce the heat to low, cover, and simmer for 15 minutes. Remove from heat and let stand, covered, for 5 minutes. Fluff with a fork and drizzle with a little olive oil and lemon juice.
Prep the greens: Wash and dry the mixed greens or chopped romaine. For extra flavor, toss lightly with olive oil, lemon juice, salt, and pepper just before serving.
Make the green harissa sauce: In a food processor or blender, combine the cilantro, parsley, jalapeños, garlic, ground cumin, ground coriander, olive oil, and lemon juice. Blend until mostly smooth, scraping down the sides as needed. Season with salt to taste. Add a bit more olive oil or a splash of water if you prefer a thinner sauce.
Make the lemon herb tahini dressing: In a small bowl, whisk together the tahini, lemon juice, water, minced garlic, chopped dill, and chopped mint until smooth. Season with salt and black pepper to taste. Thin with additional water, 1 teaspoon at a time, until the dressing is pourable but still creamy.
Make the simple lemon vinaigrette: In another small bowl, whisk together the olive oil, lemon juice, honey, Dijon mustard, salt, and black pepper until emulsified. Taste and adjust seasoning as needed.
Assemble the Cava Harissa Chicken Bowls: Add your chosen base (rice, quinoa, greens, or a combination) to each bowl. Add generous spoonfuls of hummus and tzatziki on one side. Top the base with sliced harissa chicken, dividing it evenly among the bowls. Add toppings such as diced cucumber, cherry tomatoes, pickled red onions, crumbled feta, kalamata olives, and toasted nuts. Drizzle with green harissa sauce, lemon herb tahini dressing, or simple lemon vinaigrette, or a combination of two. Garnish with fresh herbs like parsley, mint, or dill and serve immediately.