Fattoush with Queso Fresco

Name: Fattoush with Queso Fresco
Ingredients: 5 teaspoons za’atar, divided; ⅓ cup plus 3 tablespoons olive oil; 2 6-inch pitas, sliced in half crosswise, torn into 1-inch pieces; 3 tablespoons fresh lemon juice; 2 teaspoons honey; 1 romaine heart, halved lengthwise, then cut crosswise ½ inch thick; 1 small red onion, thinly sliced; 2 Persian cucumbers, cut lengthwise into quarters, then crosswise ½ inch thick; 1 cup halved cherry tomatoes; 1 cup cilantro leaves with tender stems; 1 cup parsley leaves with tender stems; ½ cup torn dill; ½ cup mint leaves; Kosher salt; 4 ounces queso fresco, crumbled; Sumac (for serving; optional)