Fill a 1-quart microwave safe bowl 1/2 full with water. Crack the eggs into it and poke a hole in the yolks with a skewer or toothpick. Microwave on high for 1 to 1 1/2 minutes until the whites are set and the yolks are still soft. Remove from the oven and set aside.
Put 2 layers of paper towels onto a microwave safe plate and place the bacon strips on top. Microwave on high power for about 3 minutes, or until crisp. Set aside.
Mix the microwave cornbread according to package directions. Cook 2 English muffin size portions using a microwave safe cup according to package directions. Remove from the cup and put onto plates.
Tear the cheese into pieces and put them into a small microwave safe bowl. Add the milk, hot sauce, and mustard and season with salt and pepper. Microwave on high for 1 minute, stirring half way through, or until the cheese is melted and smooth.
To assemble, top each cornbread muffin with 2 slices of bacon. Put a poached egg on top of each and cover each with half the cheese sauce. Garnish with chives and serve.