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.
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.
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.