Melt the butter with the olive oil in a large saute pan over medium-high heat. Add the onion, red bell pepper, and turnip. Saute for about 3 to 5 minutes, stirring occasionally.
Reduce heat and add the garlic, ham, thyme, and paprika. Season with salt and pepper, if desired, but remember the ham is salty. Stir to blend.
Cook slowly over low heat in a flat layer and stir after about 5 minutes. Repeat this process of stirring and then flattening layer to cook until hash is crispy and carmelized. Add the parsley at the last minute.
To prepare poached eggs, fill a large saute pan about halfway with water. Add the vinegar to the water. This keeps the egg white from spreading. Bring to a simmer and reduce heat to very low.
Break eggs, one at a time, into a small bowl and gently slide into the barely simmering water. Cook until desired doneness of eggs.
Carefully remove with a slotted spoon and dry on a clean kitchen towel. Serve over Ham Hash.