Make Fontina cream: In small saucepan over medium-low heat, heat white sauce until simmering. Remove from heat; stir in fontina cheese until melted. Stir in truffle oil; season to taste with salt, pepper and nutmeg. Cover and keep warm.
Thinly slice mushrooms, drizzle with 1/4 cup olive oil, season to taste with salt and pepper. Transfer to spray-coated baking sheet and roast in 350° F oven until tender, about 10 minutes. Remove and set aside.
Blanch asparagus spears in boiling water for 2 minutes. Drain; set aside.
Working in small batches, portion 3 oz. eggs into a heated spray-coated 10-inch nonstick omelet pan. Cook over medium heat about 2 minutes until omelet is firm throughout with no visible liquid remaining.
For each wrap, spread about 2 tablespoons Fontina cream onto surface of a tortilla. Place an omelet over cream. Lay 3 asparagus and 3 to 4 mushroom slices across the lower center of the tortilla. Roll up the omelet, burrito-style, and brush lightly with olive oil. Cook in a panini press for 3 to 4 minutes until browned on the outside and heated throughout. Repeat for remaining tortillas. Serve immediately.
Note: Do not let egg mixture remain at room temperature for longer than one hour (including preparation and service time).
*If using frozen or liquid whole egg product