How to Make It
Preheat oven to 400°F. Coat a 12-cup muffin pan with cooking spray.
Bring a large saucepan of water to a boil over high. Carefully lower 12 medium eggs into water with a strainer or slotted spoon. Boil 4 minutes and 30 seconds; immediately plunge into a bowl of ice water. Cool 10 minutes. Peel eggs.
Heat a small nonstick skillet over medium-high. Add sausage to pan; cook 4 minutes or until browned, stirring occasionally to crumble. Drain on paper towels.
Whisk together flours, baking powder, sugar, baking soda, and pepper in a large bowl. Whisk together buttermilk, oil, and large eggs in a separate large bowl until smooth. Add flour mixture to buttermilk mixture; stir with a wooden spoon or rubber spatula until smooth. Fold in two-thirds of sausage and 2 ounces cheese.
Divide half of batter evenly among cups of prepared muffin pan. Nestle 1 peeled cooked egg vertically into batter in each cup. Top with remaining batter. Sprinkle muffins with remaining sausage and remaining 2 ounces cheese.
Bake at 400°F on bottom rack until cheese melts and a wooden pick inserted in center comes out with moist crumbs, about 17 minutes. Remove from oven; cool on a wire rack 10 minutes. Carefully run an offset spatula or butter knife around edges to loosen muffins.