Portobello gyro filling: Remove mushroom stems and clean caps with a wet paper towel. Cut into 1/4 inch slices. In a small bowl, stir together oil, soy, lemon, garlic, and spices. Toss to coat the mushrooms. Cook mushrooms in a large nonstick skillet over medium heat for about 5 minutes, flipping to evenly cook. They should be slightly softened and deep brown when finished.
Assemble: Spread tzatziki onto one side of the pita, then add mushroom gyro filling, veggies. and feta. Fold in half and dig in!