For the vinaigrette:
Combine all ingredients except oil. Slowly whisk in oil to create an emulsion. Season with salt and pepper.
For the salad:
Sprinkle parmesan on a greased baking sheet. Bake at 350 degrees until golden and crisp. Slice cucumber thin lengthwise. Join cucumber ends together to form a 4" diameter ring. Toss spring mix with dressing and place inside the ring. Garnish with remaining ingredients.