Char poblano peppers over flame or under broiler until heavily blistered and blackened. Wrap in paper towels or put in airtight container for 10 minutes to sweat. Peel off as much papery skin as you can. Remove stems, seeds, and veins and dice. Dice onion. Peel and dice sweet potatoes.
Saute onion and peppers in olive oil over medium-high heat until they begin to soften. Add spices and stir through. Squeeze sausage meat out of casings into pan and cook, stirring and breaking up clumps, until mostly cooked, about 5 minutes.
Pile sweet potatoes into pan. Add 1/4 cup water and cover to steam, over medium heat, until potatoes start to soften, about 10 minutes. Make a well in the potatoes for each egg and crack egg into the well. Salt and pepper eggs and cover to steam until whites are set, about 5-10 minutes.
Serve hash topped as desired with any of sour cream, avocado, cilantro, corn chips, or strips of corn tortilla fried quickly in oil until crisp.