Wash the cod fillet in cold water, pat dry, and remove any bones.
Season with lime or lemon juice, paprika powder, salt, and pepper. Refrigerate until ready to cook.
Remove the outer 2 layers from the leeks and discard. Use only the white and light green parts. Cut into pieces roughly 6–8 cm long, then cut lengthwise into very fine strips.
Peel the tomatoes, cut off both ends generously, and slice into roughly 5 mm thick slices.
Heat the clarified butter in a pan over medium heat.
Add the cod fillet and fry for 3–4 minutes until lightly browned on the bottom.
Turn the fish and fry for another 2–3 minutes.
Top the fish with the tomato slices, season with salt and pepper, and sprinkle with the grated Emmentaler.
Cover the pan with a lid, reduce heat to low, and cook for 3–5 minutes until the cheese is melted and the fish is cooked through.
While the fish cooks, bring a pot of salted water to a boil and cook the tagliatelle until al dente.
Add the leek strips to the pasta water 3 minutes before the pasta is done.
Drain the pasta and leeks together in a colander.
Serve the gratinated cod fillet alongside the tagliatelle and leeks.