Preheat oven to 375 degrees. Heat olive oil in a deep pan or stock pot over medium-high heat. Add poblano halves and saute for 5-6 minutes until slightly softened. Place poblanos in the bottom of greased baking dish.
Brown beef in the same pot used for the peppers. Once browned thoroughly, drain the fat, then add the meat back into the pot. Add chopped onion and garlic and saute for 2-3 minutes until onions are translucent.
Add beans, corn, olives, and tomatoes to the meat mixture. Stir to combine. Add the taco seasoning and ¼ c. water. Bring to a boil, then reduce heat and simmer, uncovered, for about 10 minutes until liquid evaporates.
Meanwhile, crack eggs into a measuring cup. Beat slightly with a fork, then add diced green chiles. Stir to combine.
Pour meat mixture over the poblanos, and spread evenly. Pour egg mixture over the top of the beef and use the fork to press the egg mixture down into the beef, covering the top evenly.
Top with cheese. Bake covered for 30 minutes, then remove lid or foil and bake uncovered for 20 minutes longer to allow cheese to brown. Let cool for 10 minutes before serving.
