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Halve pitas. In a small bowl, combine feta cheese, white cheddar cheese, sesame seeds, 1 tsp za’atar (reserve remaining for another use), and 2 TBSP olive oil. Evenly fill pita halves with cheese mixture. Heat 2 TBSP butter and a drizzle of oil in a large pan over medium heat. Carefully add pita halves and cook, gently pressing with a spatula or heavy-bottomed pan, until cheese melts and pita is golden, 2-4 minutes per side. (Lower heat if pitas begin to brown too quickly.) Transfer grilled cheese pitas to a paper-towel-lined plate to absorb any excess grease. Serve.