Bake walnuts for 5 to 8 minutes, stirring every 2 minutes, until just toasted.
Pour into a bowl to cool.
Place apples in a bowl and toss with 1 Tbsp. vinegar. In a small bowl, whisk together remaining vinegar, mustard, shallot and sugar; season with salt and pepper.
Whisking constantly, drizzle in olive oil and continue to whisk until smoothly blended.
Place salad greens, apples and walnuts in a large bowl. Toss with dressing just before serving.