Turn on your oven-broiler to the high setting in preparation to roast the peppers, onion, and garlic. As I mentioned in my notes, you do not need to use your oven to roast the peppers and the other ingredients if you have a gas stove, you can even roast them over a regular griddle. If you use this oven version, take advantage and also use the hot oven to warm other foods.
Place the poblano peppers, onion slices, and garlic clove on a baking sheet covered with aluminum foil, roast for about 2 minutes per side. Remove garlic promptly since it will be ready quickly.
Remove from oven and lightly wrap with the aluminum foil for about 5 minutes.
Season chicken breast with salt and pepper. Heat oil in a large frying pan, once it is hot add the chicken breast to cook about 3-4 minutes per side. The cooking time will depend on the thickness of the chicken cutlets. Do not overcook, since they will keep cooking with the Poblano salsa. Remove from the frying pan, place on a plate and cover with aluminum foil.
Clean peppers removing the charred skins, open the peppers by making a slit from top to bottom and remove the seeds and veins. Reserve one half of one pepper and cut into small strips.
Place the rest of the peppers, white onion, garlic, heavy cream, milk, and chicken bouillon in your blender. Process until you have a beautiful creamy sauce.
Melt butter in the same frying pan, and pour the sauce. Gently simmer on a medium heat, allow cooking for 5 minutes, adding the chicken, and keep cooking for another 5-6 minutes. Keep the heat low to avoid the creamy sauce from curdling.