Place all 8 eggs in slightly warm tap water to bring the eggs to room temperature.
Bring enough water to a boil in a medium saucepan. Quickly transfer 6 eggs into the pan. Be careful not to break the eggs. Boil for 4-5 minutes.
In the meanwhile, add 2 cups of ice cubes to cold water in a large bowl. Once eggs are done, transfer them to the ice water. This will keep the eggs from cooking so that we will have very tender or even runny yolks inside.
Gently tap one egg against a hard surface on their wider end. Peel off the shell a little and then blow the egg like blowing a balloon, but not aggressive. This will help with peeling eggs easily. Do the same to the rest of the eggs and refrigerate them.
While eggs are chilling, let's make the muffin batter. First, remove sausage skins and cook on stove over medium high heat until brown. Break the sausage meat into small pieces with your spatula during cooking. Keep in mind that the sausage goes into muffin batter. The smaller are the pieces, the better. You might want to chop up the sausages a little before cooking. Once browned, remove from heat. Let cool.
Sift flour, sugar, salt, pepper, baking powder and baking soda all together in a large bowl.
In a separate bowl, whisk melted butter, the remaining 2 eggs, cheese, and sour cream until smooth. Gently fold wet mixture into the flour mixture. Add cooked sausage (leave out the oil from sausage) and combine until flour is gone and the batter is even.
Now go ahead and preheat your oven to 400°F.
Grease a 6-cup large muffin pan with butter or oil. Add a little flour into each tin and swirl to coat the tins well. Dump extra flour.
Scoop up 2 tablespoons muffin batter into the bottom of each tin. Make a well and press a chilled egg inches Cover the eggs completely with the remaining batter. (A spoon with a little help from your finger works perfectly well for this step). Bake for 17 minutes. Let cool for 10-15 minutes before serving. Enjoy!