Preheat the oven to 350 degrees and set the rack to the middle position.
Place the pepper halves in a casserole dish and if desired, sprinkle lightly with salt. Microwave them for 2-3 minutes or until they are tender. Remove the dish from the microwave and let the peppers cool.
Heat the oil in a saute pan over medium heat. Add the sausage and onions and saute until the sausage is no longer pink. Add the garlic and sun-dried tomatoes and saute for another 3 minutes. Remove the pan from the heat.
Drain any water from the peppers and casserole dish.
Fill each pepper about 1/3 full with the sausage mixture.
Sprinkle the cheese over each pepper (about 2 tablespoons per pepper)
Top each pepper with an egg, either by cracking it over for sunny-side up, or scramble all of the eggs and pour them evenly over each of the peppers.
Sprinkle the peppers with salt and fresh ground pepper.
Bake the peppers in the oven for about 30-40 minutes, or until the eggs are set.
When the peppers and eggs are cooked, remove them from the oven and top with the fresh sliced basil.