Put a large pot of water on high to boil and season with salt.
In a measuring cup, add oil, egg yolks, lemon zest and juice, Pardammer cheese and herbs.
Once boiling add pasta and cook just until al dente, about 3-4 minutes, stir in arugula then drain and return pasta and greens to pot.
Immediately add the oil and cheese mixture and stir through gently until it melts, thickens and becomes a smooth sauce. (You can turn heat on low for a minute if it doesn't have enough heat to melt cheese but stir and do not let it get too hot or boil)
Meanwhile preheat large frying pan to medium high. Season halibut with salt and pepper. Add olive oil to pan and add halibut once oil is hot. Panfry 2-3 minutes per side until just cooked through.
Place the pasta on 4 plates, top with halibut and serve with arugula salad.