Preheat a grill or grill pan over medium-high heat and spray with cooking spray.
With a spoon, gently scrape out the dark inside of the mushroom caps, being careful not to break the cap. Brush both sides of the mushroom caps with oil and sprinkle with salt. Grill the mushrooms over a medium-high heat, until they are tender and their juices begin to release, about 7 minutes per side. Transfer to a plate, top side down.
On the same grill or grill pan, cook the Canadian bacon over medium-high heat, until they are warm and grill marks have formed, about 30 seconds on each side. Place 1 piece of the bacon into each of the mushroom caps.
Separate the whites of 4 of the eggs into a medium bowl and discard the yolks or save them for another use. Add the remaining 4 whole eggs to the bowl with the whites, add the water and whisk until combined. Cook the eggs in a medium nonstick skillet over a medium-low heat, stirring frequently, until the eggs are done, about 3 minutes. Season with salt and pepper. Spoon 1/4 of the scrambled eggs on top of the Canadian bacon in each the mushroom caps. Drizzle 1 teaspoon of pesto over each and top with some basil ribbons and 1 teaspoon of Parmesan.