Preheat oven to 350 degrees . Grate half a garlic clove; chop the remaining garlic and set aside.
Stir 1/2 cup yogurt, 1 tbsp olive oil and 1 tbsp water into the grated garlic; season with salt and pepper.
in a bowl, whisk together the eggs, the remaining yogurt, 2 tbsp water and 1/4 tsp pepper. Stir in the pita slices and set aside to soak.
In an ovenproof skillet, combine the remaining 3 tbsp olive oil and the chopped garlic. Cook over medium heat, stirring, for 1 minute. Add the chard and cook until wilted, 2 minutes.
Stir the chard and 2 cups cheese into the egg mixture; return to the skillet in an even layer. Cover and cook over medium-low heat until set at the edges, 3 minutes.
Uncover, sprinkle with the remaining 1 cup cheese, transfer to the oven and bake until golden, 17 minutes. Serve with the lettuce topped with the yogurt dressing.