Preheat oven to 425 degrees.
Heat the oil in a large nonstick skillet over medium-high heat. Add the sausage, and cook, stirring and breaking up with a wooden spoon, until browned and cooked through, 8 to 10 minutes. Remove from the heat, and use a slotted spoon to transfer the sausage to a plate.
Reserving 2 tablespoons of drippings in the skillet (drain or add oil as needed), return it to medium-high heat. Whisk in the flour, and cook, whisking frequently, until the mixture becomes loose and turns a light tan color, 1 to 2 minutes. Slowly whisk in the milk, 1/2 teaspoon pepper and 1/4 teaspoon salt. Simmer, whisking frequently, until the sauce has thickened to the consistency of thin gravy, 6 to 8 minutes. Return the cooked sausage to the skillet, and stir. Remove from the heat, cover and set aside.
Place the Naan bread on a baking sheet. Distribute the cheese on all pieces of naan bread. Make a well in the center of each bread, crack an egg and let the egg rest in the center of the Naan bread.
Bake for 8-9 minutes. The egg whites should no longer be clear and white at this point.
Leaving the naan bread in the oven, turn on the Broil settting and continue baking for 2 additional minutes.
Serve with the sausage gravy on top.