Put a large casserole or saucepan over a medium heat, add the oil and chorizo, and fry for 5-7 minutes or until lightly charred. Remove the chorizo with a slotted spoon and set aside. Add the shallots and a pinch of salt, and fry gently for 5-7 minutes until soft and translucent. Add the paprika and potatoes, cook for 1 min more, then add the barley and stock and bring to the boil. Stir well, then reduce the heat and cook for 20 mins. Add the broccoli and cooked chorizo and cook for 2-3 mins with the lid on or until the broccoli is tender.
Meanwhile, finely chop the parsley and garlic, and combine with the lemon zest in a bowl. Set aside.
Stir the lemon juice through the stew and season to taste. Ladle into shallow bowls and top with the fragrant herb and garlic mixture.