Remove the sausage from the casings. Crumble it into a large, oven-safe pan (preferably cast iron) set over medium-high heat. Cook, stirring occasionally until the sausage is golden brown and cooked through – about 8 minutes. Transfer the sausage to a plate.
Return the pan to the stove and reduce the heat to medium. Add the onion and garlic; cook 1-2 minutes. Add the potatoes, poblano, and red pepper; cook until the potatoes are browned and crispy – about 10 minutes. Stir in the eggplant, mushrooms, and water. Cook for 10 minutes, or until the water is evaporated and the vegetables are cooked soft. Stir in the kale.
Meanwhile, heat the oven to 400ºF.
Crack the eggs onto the hash (At this point, you can divide the hash between six ramekins to make individual portions.) Bake 10-12 minutes, or until the whites are completely set.