Slice chicken breasts in half lengthwise to create thinner slices, then pound to 1/2 inch thickness using a meat mallet.
Pat chicken dry and season both sides with salt, pepper, oregano, and dill.
Place 1/3 cup Greek salad dressing and chicken in a gallon freezer bag; seal and marinate at room temperature for 20 to 30 minutes.
Whisk together all sauce/dressing ingredients except cornstarch and set aside; keep liquids cool to prevent cornstarch activation.
Heat oil in a skillet over medium-high heat, sear chicken 3-4 minutes per side until golden and cooked through, then let rest for 10 minutes before slicing.
Add white wine to the skillet and cook over medium heat, scraping browned bits off the pan with a silicone spatula, reduce by half for about 3 minutes.
Add garlic and prepared sauce mixture to the skillet, bring to a boil until thickened, then remove from heat and refrigerate until ready to serve.
Assemble bowls with lettuce in the center, topped with sliced chicken; arrange chickpeas, tomatoes, cucumber, olives, feta, lemon slices, and pita around edges.
Stir sauce and drizzle over the bowls, then garnish with chopped parsley before serving.