Arabic Fattoush Salad

Name: Arabic Fattoush Salad
Ingredients: 1 tablespoon vegetable oil for frying; 2 small (4 inch) pita breads, torn into pieces; 1 large English cucumber, finely diced; 3 cups halved grape tomatoes; 0.75 cup chopped Italian parsley; 0.75 cup chopped fresh mint; 0.5 red onion, finely diced; 2 tablespoons extra-virgin olive oil, or to taste; 1 tablespoon fresh lemon juice, or to taste; 1 teaspoon ground sumac, or to taste; 1 clove garlic, crushed (or more to taste); kosher salt and freshly ground black pepper to taste; 1 ounce sheep's milk feta cheese