First take a look at your poblanos and figure out the best side to lay them on so that you can cut the top off the pepper and an egg will say inside. Then slice the top off of one side of the pepper. Then use a small knife to remove the seeds and membranes.
Heat the water and olive oil in a skillet over medium heat. Place the poblano peppers in the skillet inside facing down. Cover the skillet and steam the peppers for 4 minutes.
While the peppers steam, shred the cheese.
Then flip the peppers over, sprinkle the cheese inside, and crack and egg inside. Repeat with all of the peppers. Sprinkle salt and pepper over. Put the lid back on the pan, and cook for 4-5 minutes, until the whites have fully cooked. The yolks should still be runny. Serve immediately.