Preheat oven to 400 degrees.
Mix flour, paprika, and salt and pepper together. Season hake portions lightly with salt and pepper, then dredge each portion in seasoned flour.
Heat oil on medium-high heat in a 10- or 12-inch non-stick sauté pan. Place fish in pan and sauté until golden brown, turning once to cook both sides. Work in batches if all fish doesn’t fit at once, but leave space between the pieces of fish. Transfer to a sheet pan and set aside.
In a 7½- or 8-quart sauté pan with straight sides and a lid, heat oil over medium high heat.
Add fennel and sauté until it just starts to turn translucent, stirring frequently.
Add garlic and red pepper flakes. Continue cooking until garlic starts to turn golden, then add diced tomato and cook until tomatoes start to soften.
Add white wine and reduce by half.
Add chorizo and cook until oil begins to release.
Add diced carrots, cook for a few minutes, then add clam juice and bay leaf. Bring to a simmer. Simmer for 10 -12 minutes.
Put sautéed hake filets in the preheated oven. Bake fish until cooked through (12-20 minutes depending on the thickness of the filets). Fish will be flaky when cooked through.
Place clams in a single layer over broth and cover tightly with a lid or foil. Let the clams steam in the broth until they open (5-10 minutes). Taste broth and add water if too salty.
Finish with squeeze of fresh lemon juice, butter and any herbs you desire such as parsley, cilantro or basil.
Divide clams and broth into 4 pasta or shallow bowls. Top with hake and enjoy!