Heat a large pot and add the bacon. Cook on medium-low until crisp and the fat is rendered. Remove to a plate.
Pour out all but 2 tablespoons of the fat.
Add the chorizo and increase the heat to medium high. Cook, stirring frequently, until it is browned.
Reduce the heat to low and add the onion. Cook for 5-6 minutes, or until it is soft and a little browned around the edges.
Add the garlic and tomato paste. Cooke for 1 minute.
Add the smoked paprika, paprika, and cayenne. Cook for 20-30 seconds.
Pour in the chicken stock. Add the potatoes and return the bacon to the pot.
Increase the heat and bring the soup to a boil. Then lower the heat so that the soup is simmering. Simmer the soup for about 20 minutes. The potatoes will be soft and and tender.
Add the cream and stir in. Taste the soup and add salt, pepper, and more cayenne to taste.
Stir in the parsley and serve.