Season eggplant slices with salt, to taste. Place in a colander and let rest for approximately 20 - 30 minutes.
Preheat electric skillet to 400 degrees.
Place all dressing ingredients in a small jar, cover with lid and shake vigorously to combine. Set aside.
Add eggplant to skillet and cook for 3 - 4 minutes until browned and softened. Turn eggplant and cook for an additional 3 - 4 minutes. Remove eggplant
When eggplant is cool enough to handle, but into medium dice and place in a bowl.
Add chopped tomatoes and pour dressing over top. Toss to combine.
Clean griddle and reheat over medium heat. Toast pita bread for 3 minutes, turn over and place 1 ounce mozzarella on top. Cook for an additional 3 - 4 minutes, until mozzarella is slightly melted.
To serve, place warmed pita bread with mozzarella on plate. Top with ¼ of salad greens and then with ¼ of eggplant mixture. Garnish with shaved pecorino Romano cheese.