Set aside ¼ cup of olive oil for the pita bread. Place all remaining dressing ingredients in a blender and blend until fully emulsified. Add salt and pepper to taste.
Brush pita bread loaves with olive oil and toast them on a grill. (This can also be done in an oven or toaster oven.) Cut each toasted loaf in half and then into wedges. You should be able to get 8 wedges from each loaf.
Toss arugula with ⅓ of the salad dressing. Arrange salad ingredients, including pita bread, on plates as desired. Remaining dressing can be drizzled over the arranged salad.