Preheat oven to 375°F. Place lobster mushrooms in a small bowl, cover with boiling water and let soak for 20 minutes. Strain liquid from mushrooms through a colander.
In a large frying pan, heat the butter and canola oil over medium heat. Add shallots and cook for 1 to 2 minutes. Add the lobster mushrooms, wild mushrooms, garlic, basil and scallops, season with salt and pepper and cook over high heat for 2 to 3 minutes.
Meanwhile, whisk the eggs in a large bowl seasoned with salt and pepper.
Slowly pour the egg mixture into the frying pan and cook over medium low heat, gently stirring the mixture. When the frittata is partly cooked (7-10 minutes), sprinkle the top with the Asiago cheese and place the pan in the preheated oven.
Bake the frittata for approximately 20 – 25 minutes until golden. Remove from the oven to check for doneness. Shake the fry pan, the egg mix should not move. Let the frittata rest for 5-10 minutes and cut into wedges.