In a mixing bowl, combine chopped parsley, fresh tarragon, minced shallot, and diced cornichons. Add crumbled egg yolk, diced egg white, white wine vinegar, a pinch of salt, Dijon mustard, and mayonnaise. Stir until well combined. Set aside for about 30 minutes.

In a large mixing bowl, whisk together the cake flour and baking soda. Gradually pour in the cold beer while stirring continuously until smooth. Let the batter rest for 15-20 minutes.

Rinse the halibut fillets under cold water and pat them dry thoroughly. Season both sides with salt.

In a frying pan or deep fryer, heat oil to 350°F (175°C). Test with a spoonful of batter.

Dip each seasoned halibut fillet into the batter and carefully place in the hot oil. Fry 4-5 minutes until golden brown.

Plate the crispy halibut with tartar sauce and thick-cut fries or potato wedges.