Sauté the Spinach: In a grill pan, heat 1 tablespoon of extra virgin olive oil over medium-high heat until shimmering. Add the baby spinach and sauté for a couple of minutes, tossing occasionally, until wilted. Remove from the pan and set aside. Turn off the heat for now.
Assemble the Sandwiches: Warm the pita pockets slightly to prevent them from breaking when opened. Spread feta cheese evenly on the bottom of each pita, followed by a layer of basil pesto. Add a spoonful of the wilted spinach, then top with fresh mozzarella slices and sun-dried tomatoes.
Grill the Pitas: Reheat the grill pan over medium-high heat. Brush both sides of each pita pocket with extra virgin olive oil. Arrange the pita sandwiches in the heated pan so they all make direct contact with the hot surface. Cook for 1 to 2 minutes on one side, pressing gently on the sandwiches with the back of a spatula. Flip them over and cook for another couple of minutes, applying pressure again, until the cheese is melted and the pitas have developed char marks. Adjust the heat as needed to avoid burning while ensuring the cheese is fully melted. You may need to briefly cover the pan to help the mozzarella melt completely.