Place the chicken strips in a mixing bowl. Add the za'atar, salt and pepper, and garlic powder; toss to coat evenly.
Add the juice of one lemon and 3 tablespoons olive oil to the seasoned chicken and toss again to combine.
Heat an 8-inch searing pan or skillet over medium-high heat until hot, then add the chicken in a single layer and cook 5–7 minutes per side until cooked through and browned; remove and set aside.
Pat the halloumi strips dry with paper towels. Heat about 1/3 cup olive oil in a non-stick skillet over medium heat.
Fry the halloumi strips 2–3 minutes per side until golden and slightly crisp, then transfer to paper towels to drain excess oil.
Arrange arugula on a serving platter, top with sliced avocado, strawberries, and sweet bell peppers. Add the cooked chicken and fried halloumi on top.
Drizzle the salad with olive oil and additional lemon juice to taste, then sprinkle with minced parsley and serve.