01 - Preheat the oven to 350°F (180°C) if finishing the hake in the oven.
02 - Pat the hake fillets dry with paper towels and season both sides with sea salt and freshly ground black pepper.
03 - Warm 2 tablespoons of olive oil in a large non-stick skillet over medium-high heat.
04 - Place hake fillets skin side down in the pan and press gently with a spatula for 1 minute to ensure crispiness.
05 - Cook the skin side for 3 to 4 minutes until golden and crisp, then carefully flip and cook the other side for 2 to 3 minutes until just cooked through. For thicker fillets, transfer to the oven and cook for an additional 3 to 4 minutes. Remove and rest skin side up.
06 - In a separate skillet, heat 2 tablespoons of extra virgin olive oil over medium heat.
07 - Add ground beef and cook while breaking it up with a spoon until browned and slightly crisp, about 5 minutes.
08 - Stir in smoked paprika, sweet paprika, ground cumin, dried oregano, garlic powder, cayenne pepper (if using), and sea salt. Cook for 1 minute until fragrant.
09 - Add tomato paste and red wine vinegar, cooking for another 1 to 2 minutes to blend flavors.
10 - Stir in gluten-free breadcrumbs and cook for 2 to 3 minutes until the mixture becomes crisp and crumbly. Adjust seasoning if necessary.
11 - Spoon the chorizo-style beef crumb onto warmed plates. Top each with a crispy hake fillet, skin side up. Garnish with chopped parsley and lemon wedges.