Heat 1 tablespoon of the olive oil in a large pot and add basil, oregano, onion and garlic. Saute until onions soften and become translucent
Add ground pork and cook until browned, then stir in tomato paste, Loosen up the mixture with water. Add cracked bulgur wheat, then turn heat down and cover.
While filling simmers, prep the peppers for baking. Slice the tops off of two large bell peppers and scrape the seeds out of them. Discard the tops. Set the peppers in a square baking pan lined with foil.
Spoon pork and grain filling into hollow peppers. Top with cheese if you like. Monterey jack or mozzarella work well. Bake at 350 degrees for 40 minutes.
When the peppers are done, pull them out of the oven to cool for about ten minutes. Put each pepper on a plate, and slice each one down the side to reveal filling.
Pour the remaining tablespoon of olive oil into a small frying pan to heat. Fry each egg separately, then place one on each stuffed pepper. Serve immediately.