In a medium pot, fill with about 2 qts water, add 2 tbsp vinegar, 1 tsp of kosher salt, and bring to a boil. Add diced potatoes and cook until barely tender about 4-5 minutes. Remove from the heat, strain in colander, and set aside. 

Preheat oven to 375 degrees F

In a 12 inch cast iron skillet, over medium heat, add 2 tbsp olive oil and diced chorizo. Cook for 8 minutes until chorizo has reduced and browned. Using a slotted spoon, remove the chorizo and set aside, but leave behind the oils and tiny bits. 

In the same skillet, raise the heat to medium-high, add 3 tbsp olive oil and add the drained diced potatoes. Add 1/4 tsp kosher salt, fresh ground black pepper, and optional red pepper flakes. Cook the potatoes for 15 minutes, tossing/stirring occasionally until potatoes have crisped on all sides. When 5 minutes remain, add the 1 tbsp of unsalted butter and allow to melt and toss the potatoes.

Return the chorizo to the skillet, mix with the potatoes, and form four small wells. Carefully crack four eggs into each of the four wells, season eggs with salt/pepper and sprinkle cheddar cheese over the potatoes. Place into the oven and bake for 10 minutes. Whites should be set and the yolks runny. Remove from oven, top with fresh green onions, and serve!