• Add the diced potatoes to a medium size pot, add water to cover by an inch and stir in the vinegar. Bring to a boil then reduce heat to medium, cook until just fork tender, about 10 minutes, don't over cook them. when just fork tender, remove from heat and drain. Set aside. (I use a French fry cutter first, then slice the fries into cubes.)
  
• Clean the leaks by cutting off the root ends and the the dark green leafy part. Rinse, then thinly slice into rings, add the slices to a bowl of cold water and stir and agitate the water to remove any sand or dirt between the various layers. Remove the slices and drain any water from them. If there is a lot of grit in the water after you removed the slices, pour that out and repeat the process just to be sure the leeks are cleaned well.
  
• Heat the olive oil in a large pan, a cast iron pan would be ideal but I used my good marble pan for this. When hot, over medium heat, add the sliced leeks and cook until just soft, about 5-6 minutes or so.
  
• Add the diced potatoes, garlic, paprika, and salt, and cook until the potatoes are golden brown.
  

For Eggs Cooked Seperately

• When the potatoes are golden brown, place the hash on plates to serve. Same pan, crack in your eggs and cooked to your desired likeness. Place an egg on each plate of hash, serve.

For Eggs Cooked on the Hash

• Lower heat to low. Use a large spoon and make 4 to 5 indentations in the potatoes. Crack an egg into a small bowl, gently pour the egg into an indention in the hash, repeat for the rest of the eggs. The reason I state use a bowl, if you crack an egg directly into the hash but a yolk breaks, the egg will just disappear into the hash, still very good, not visually appealing.
  
• Once the eggs are on the hash, season them with salt and pepper to your liking, and cover the pan with a lid. Check the eggs every minute or so to get perfect sunny side up eggs.
  
• Serve by scooping out a portion of hash with the egg already on top.