Fill a medium saucepan halfway with water and bring to a simmer.
Preheat a medium-sized skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the chorizo and cook, stirring frequently, about 5 minutes. Add the onion, pepper and potatoes. Let the potatoes brown up a little and get crispy around the edges, this will take about 8-10 minutes. Add the turkey and heat through.
While the potato mixture is cooking, pour vinegar into the simmering water. Crack an egg into a small bowl and gently pour it into the simmering water. Repeat with the remaining 3 eggs. Cook the eggs for about 2 minutes for runny yolks, or about 4 for solid yolks. Do not allow the water to boil. Carefully remove the eggs with a slotted spoon to a towel-lined plate to drain. Plate the poached eggs over top of the turkey hash. Break into the egg and let the yolk run over the top so it acts as a sauce. Yum-O!