1. In an 8- to 10-inch frying pan over medium heat, stir walnuts often until lightly browned, 6 to 7 minutes. Remove from heat and let cool.
2. In a large bowl, whisk together oil, vinegar, shallots, garlic, mustard, sugar, and 2 tablespoons of the toasted walnuts. Stir in chives and salt and pepper to taste.
3. Rinse apples; quarter, core, and thinly slice lengthwise. Add apples, red onion, and mixed baby greens to dressing and mix to coat. Add half the cheese and mix gently. Mound salad equally on 8 to 10 plates. Sprinkle with remaining cheese and toasted walnuts. Add more salt and pepper to taste.