To prepare the hash: In a medium saucepan, cover the potatoes with cold water and bring to a boil over high heat. Reduce the heat and simmer until tender, about 25 to 30 minutes. Drain the potatoes, peel and cut into 1/2-inch cubes. Season the chicken breast with salt and pepper and place in a saucepan of simmering water. Poach for 10-12 minutes or until cooked through. Cut each breast into 1/2-inch cubes. Place the potatoes, chicken, scallion, cilantro, chipotles and honey in a large bowl and mix gently until combined, season with salt and pepper. Form into 4 equal-sized patties. Heat the oil in a large saute pan until just smoking. Season the patties with salt and pepper to taste and saute the patties on each side until golden brown. Keep warm.
To prepare the poached eggs: Heat the water and vinegar until simmering in a large frying pan. Break each egg into a cup and gently add to the water. Poach for 4 to 5 minutes, or until the yolk is nearly cooked. Remove the eggs from the pan with a slotted spoon to drain the liquid and top each hash patty with 1 poached egg and some Green Chile Hollandaise.
Green Chile Hollandaise:
Place the yolks, salt, pepper in a blender and mix until smooth. Slowly, drop by drop add the warm butter to the mixture and blend until emulsified. Place in a bowl and fold in the chopped poblano peppers. Serve immediately or place the bowl over a pot of simmering water to keep warm, stirring occasionally.