Line a baking pan with aluminum foil. Put the chile poblanos on the lined baking pan and broil for 10 minutes until charred. Use tongs to flip the chile to the other side. Broil for another 10 minutes. Depending on the thickness of the chile, broil for another 5 minutes on the sides that weren't broiled.
Transfer the broiled chile to a brown paper bag and fold to close. Leave in the bag for 5-10 minutes until cooled. You may want to put a plate underneath the paper bag to capture any moisture.
Peel the blackened skin off the chile as much as you can and remove the seeds. Cut the chile into strips at least 1-inch thick. Depending on your spice tolerance, you can leave some seeds.
In a large skillet, add olive oil over medium heat. Sauté the garlic and onion until softened. Add the diced potato and sauté for 5 minutes until slightly softened.
Add the water the chicken bouillon seasoning. Cover and simmer over medium-low heat for 13-15 minutes until the potatoes are fully cooked.
Add the cut chile strips and the cheese. Stir to combine until the cheese is melted. Season with salt and pepper to taste. Enjoy!