Heat the oil in a large skillet over moderate heat. Add the leek and onion and saute until soft, about 5 minutes. Add the garlic, salt and pepper and saute another minute. Add the carrots, potatoes and scant 1/4 cup water to skillet. Cover and cook until vegetables are tender, 5 to 7 minutes.
To the vegetables in the skillet, add the red pepper, poblano chile and mushrooms and saute until softened, 3 to 5 minutes. Add the cilantro and mix to combine, then turn the heat to high to lightly brown the hash.
Meanwhile, poach the eggs: Bring 4 cups of water and the vinegar to a simmer in a deep saute pan. One at a time, tip each bowl over the water and let the eggs fall gently into the water. After 1 to 2 minutes, remove each egg with a slotted spoon and drain on paper towels.
Divide the vegetable hash among individual plates, making a well in the center of each. Using a slotted spoon, carefully place a poached egg in the center of the hash. Serve warm with Salsa Roja.
c.1997, M.S. Milliken & S. Feniger, all rights reserved