Preheat oven to 425F.
Cook bacon in a pan until fat renders and bacon crisps, about 5-7 minutes. Remove bacon and place on a paper towel lined plate. Drain off some of the bacon grease but keep a tbsp or two to cook the veggies in.
Add mushrooms to the pan and cook until browned, about 5 minutes.
Add the greens to the same pan with the mushrooms and cook 3-4 minutes or until wilted. Season everything with salt and pepper.
Add the bacon back to the pan with the veggies, toss to combine, and remove from the heat.
To assemble each pizza, sprinkle a piece of naan with about ¾ cup of shredded cheese and top with half of the veggie and bacon mixture. Create 1 to 2 wells in the center of the veggies and place a cracked egg into each well. Season the egg(s) with salt and pepper.
Bake for 11-14 minutes, depending on how set you want your egg (13 minutes for cooked white and slightly jammy yolk). Remove pizza from the oven and top with chili oil, if desired.