Add potatoes to a medium sized pot and cover with enough water to submerge. Cover with a lid and cook on medium-high heat until it reaches a boiling point (this could take about 15 minutes or more). Lower the heat to medium and let cook for 3-5 minutes, until tender (the fork should pierce through the potato with light force; you don't want it to be mushy). Drain in a colander.
While waiting on the potatoes, start working on the chorizo!
Preheat olive oil in a large skillet over medium-high heat.
Crumble the chorizo into the pan. Saute the meat until browned and the fat has rendered; about 10 minutes.
Using a slotted spoon, transfer the meat over to a dish lined with paper towels to absorb extra oil; leave the rendered fat in the skillet.
Add the pre-boiled potatoes and onions to the skillet over medium-high heat and saute for about 15 minutes; until the potatoes are fully cooked. Season with 1 teaspoon kosher salt and stir to combine. Add the cooked chorizo back to the skillet and cook for an additional 2-3 minutes. Add paprika, freshly ground black pepper, and if necessary, more salt to taste.