Place the potatoes in a pot and cover them with water. Place the pot over high heat and bring to a boil. Cook them for about 12 minutes, or until they are fork tender. Once they are cooked, drain the potatoes and return them to the pot, then put them over medium heat for about 1 minute to dry them out. turn the heat off and add the chives, butter, half of the parsley, salt, pepper and hot sauce to taste. Stir the potatoes until the butter has melted, then transfer to a serving platter.
While the potatoes are cooking, preheat a large skillet over med-high heat with 2 T of the olive oil. Season the chicken with the salt, pepper, thyme and paprika. Add the chicken to the skillet and cook for 5 to 6 minutes per side, or until it is cooked through. Remove the chicken to a plate and cover it with aluminum foil to keep them warm. Return the skillet to the cooktop over med-high heat. Add the remaining 2 T of olive oil and the chorizo and cook, stirring frequently, for about 2 to 3 minutes. Remove the chorizo from the skillet to a plate using a slotted spoon and reserve.
Turn the heat up to high and add the mushrooms to the same skillet. Spread them out in an even layer and resist the urge to stir for a couple of minutes so that the mushrooms can start to brown. Once they are brown, go ahead and shake the pan up, stir and continue to cook them for 2 minutes more. Then add the onions, garlic and reserved chorizo and season with salt and pepper. Continue to cook, stirring occasionally, for about 3 minutes more, or until the onions start to look tender. Add the sherry and cook for 1 more minute. Then add the chicken stock and bring to a boil. Simmer for about 2 minutes. Add the remaining parsley and stir it to combine, then taste and adjust the seasonings with salt and pepper.
To serve, arrange the cooked chicken breasts on serving plates, top with the mushroom-chorizo sauce, and serve the butter and herb spubs alongside.