Place eggs in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, cool, peel and chop. Place bacon in a large, deep skillet. Cook over medium high heat until evenly brown. Drain, crumble and set aside. In a medium sized saucepan, melt butter over medium heat. When butter has melted, whisk in the flour. Stir until all lumps have dissolved. Slowly pour in the milk, stirring constantly, until thickened. As gravy begins to thicken, add chopped eggs and 2 cup cheese. Cook 3 to 5 minutes to melt the cheese and heat through. Stir in the sour cream, cayenne, salt and pepper; stir until heated through. Keep warm over low heat until ready to serve (do not boil). Slice cornbread pieces and lay open on serving plates. Ladle a generous amount of egg mixture over the cornbread, top with remaining shredded cheese, crumbled bacon, and green onion.