Preheat oven to 400°F. Lightly grease a standard 12-cup muffin pan with cooking spray. Set aside.
Bring a large saucepan of cold water to a boil over high heat. Using a slotted spoon, carefully lower 12 medium eggs into the boiling water. Boil for 5 minutes and then immediately plunge the eggs into a large bowl of ice water. Cool for 10 minutes before carefully peeling under water. Set aside.
In a large bowl, whisk together the flours, baking powder, sugar, baking soda, and pepper. In a separate bowl, whisk together the buttermilk, oil, and large eggs until smooth. Make a well in the center of the dry ingredients and then pour in the wet; stir with a wooden spoon or rubber spatula until smooth. Fold in the scallions, two-thirds of the bacon and half of the cheese.
Divide half of the batter evenly among the prepared muffin pan. Nestle 1 peeled boiled egg vertically into batter in each cup. Top with remaining batter and sprinkle with the remaining bacon and cheese.
Bake at 400°F until golden brown and a toothpick, inserted into the bread part of the muffin, comes out clean, about 17 to 20 minutes. Remove from oven; cool on wire rack for 10 minutes. Carefully run an offset spatula or butter knife around the edges to loosen. Serve warm and enjoy!