Bring a pot of water to a boil then add the chopped potatoes. Simmer for 4 to 5 minutes, then drain in a colander and set aside.
In a sauté pan, fry the onions in the heated olive oil (sprinkle a little salt on the onions) for about 5 minutes or so. Do not let them brown. Next, add the paprika, cayenne, and white pepper and stir.
Add the flour, stir and continue to cook for about 3 minutes, then slowly add the chicken stock.
Stir continuously until all the stock has been added, then simmer for 8 to 10 minutes, stirring often.
Remove from heat and process with an immersion blender until smooth (or process in a blender) and set aside.
Heat enough oil to deep fry the potatoes, then add half at a time, unless you are using a very large pot or fryer. Fry until golden brown, then place on a paper-towel lined plate or bowl. Repeat with the next half.
There are several ways to serve Patatas Bravas. Sometimes, the potatoes are served on a plate with the salsa brava on the side, along with some mayonnaise or aioli sauce. Other times, the sauce is mixed with a little mayo to create a less spicy sauce. Either way, these sauces can be poured over the plate of potatoes or squeezed over them from a condiment bottle. I don't think any manner is more or less "correct" than another.