Angel Bakeries Pita Pillows stands apart from other pitas. They are indeed soft and fluffy like pillows, pliant and thick, and open wide to stuff full like a purse rather than a pocket. Baked in Carteret, N.J., in an old White Castle bun plant, their genesis is the Angel Bakeries in Israel, a chain whose first bakery opened in 1927. For decades, Angel has shipped pitas frozen to restaurants and markets in the United States.