To Prepare the Dressing: In a small bowl, mash 1 tablespoon of the cheese into the buttermilk with a fork until blended. Stir in vinegar, salt, pepper, remaining blue cheese, and parsley. Cover and refrigerate (can be made 1 day ahead).
To Prepare the Chicken: Cut chicken breasts lengthwise into 3 strips; cut each strip into 3 pieces. In a bowl, whisk buttermilk, garlic, cayenne, and salt; add chicken. Cover and marinate in refrigerator at least 2 hours and up to 6.
Drain chicken; coat with breadcrumbs. Cook chicken in oil in a large nonstick skillet over medium heat about 7-10 minutes, turning pieces frequently, or until cooked through and golden. Drain on paper towel.
To Make the Salad: In a bowl, toss salad ingredients with 1/4 cup dressing; place on 4 plates. Top with chicken. Drizzle with remaining dressing.