Preheat oven to 425°F. Grease a large muffin tin with avocado oil and set aside.
Fill a medium saucepan about halfway with water and bring to a boil over medium heat. Add in 6 of the eggs using a slotted spoon and boil for 6 minutes.
Prepare an ice bath by filling a medium bowl with ice and water. Add the boiled eggs to the ice bath. When cool to the touch, peel, pat dry and set aside.
While the eggs are boiling, prepare the batter. In a medium bowl, whisk together the flour, baking powder, soda, salt, and pepper. Set aside. In a large bowl, whisk together the remaining two eggs, buttermilk, and avocado oil.
Add the dry ingredients into the wet and fold until just combined. Add in the cheeses and scallions and stir to combine.
Add a little flour to a shallow dish and roll the eggs in to lightly coat. Using a spoon, fill the muffin tin up halfway with batter. Nestle an egg into each muffin tin cavity with the egg set vertically. Top with more batter to cover the eggs.
Sprinkle tops with a little parmesan and bake for about 15-17 minutes, until puffed and golden. Serve immediately.