Preheat oven to 375°F. Toss pita pieces with 1 tablespoon of the oil, 2 teaspoons of the sesame seed, paprika and sea salt in large bowl. Spread evenly in large baking pan.
Bake 5 to 10 minutes or until pita are crisp. Set aside to cool.
Meanwhile, heat remaining 1/4 cup oil in medium skillet on medium heat. Add garlic; cook and stir 1 minute or until lightly browned. Set aside to cool.
Toss cucumber, cherry tomatoes, pepperoncini, green onions, lemon juice, mint, thyme, and garlic and oil mixture in large bowl. Cover.
Refrigerate 1 hour to blend flavors. Add pita; toss to mix well. Sprinkle with remaining 1 teaspoon sesame seed. Serve immediately.