Preheat oven to 350 degrees F (180 degrees C).
Line baking sheet with a Silpat or parchment paper.
Place 2 tablespoons of grated Parmesan cheese in piles on the baking sheet, no more than 4 per sheet. Bake for approximately 5 to10 minutes, watching closely, until melted and bubbling.
Once cheese is golden remove pan from oven, allow to sit for only a minute until cool enough to handle. Spray the bottom of a bowl or espresso cup with vegetable spray. Lift the Parmesan disc up with a spatula and place over the bottom of the bowl. Gently mould shape with hands. Be careful, cheese will be hot. Cool completely before removing.
Handle with care, it will be fragile.
In a food processor pulse walnuts, garlic and shallot. Add Dijon mustard and balsamic vinegar.
Slowly drizzle in olive and vegetable oil. Add mayonnaise to finish. Season with salt and pepper.
To serve, place Parmesan basket on plate, fill with assorted greens, drizzle dressing on top of greens.