1. Preheat oven to 425°.
2. Combine 1/2 cup buttermilk and egg white in a shallow dish. Place panko in a shallow dish. Dip chicken in egg white mixture; dredge in panko. Sprinkle with 1/4 teaspoon kosher salt and 1/4 teaspoon pepper.
3. Heat an ovenproof skillet over medium heat. Add canola oil; swirl to coat. Add chicken. Cook 4 minutes; turn over. Bake at 425° for 14 minutes or until done. Let chicken stand 10 minutes; slice crosswise.
4. Combine pita, cherry tomato halves, basil, onion, and olives in a large bowl. Combine vinegar, Dijon mustard, 1/4 teaspoon kosher salt, and 1/4 teaspoon freshly ground black pepper, stirring well with a whisk. Gradually add olive oil, stirring constantly with a whisk. Drizzle dressing over pita mixture; toss to coat. Arrange about 1 1/2 cups salad on each of 6 plates; divide sliced chicken evenly among servings. Top each serving with 1 tablespoon crumbled feta cheese.