Prick the potatoes all over with a fork and place them on a baking sheet. Bake until knife-tender, 30 to 45 minutes. (If you like, you can do this the night before and refrigerate the potatoes until ready to cut and fry.) Cut each potato into 6 or 8 wedges, depending on size.
Heat about 4 inches of oil in a large, heavy pot until a deep-frying thermometer registers 375 degrees F. In two batches, fry the potato wedges until crispy and golden brown, 4 to 5 minutes. Drain on paper towels and season with salt. Set aside and keep warm.
In a large bowl, combine the 2 cups flour, cornstarch, baking powder and 1 1/2 teaspoons salt. Make a well in the center and add the egg yolks. Gradually whisk in the club soda, working your way out from the center to form a smooth batter.
Season the 1 cup flour with salt and pepper. Dredge the fish fillets on both sides in the seasoned flour and then dip them in the batter. Fry a few pieces at a time until crispy and golden brown, 4 to 5 minutes. Drain on paper towels and season with salt.
When the fish is done, place some parsley leaves in the hot oil and fry until crispy and slightly translucent, 15 seconds. Drain on paper towels.
Serve the fish with lemon halves, crispy fried parsley leaves and homemade tartar sauce.
Combine the mayonnaise, sour cream, cornichons, capers, parsley, tarragon and lemon juice in a small bowl. Refrigerate for 10 to 15 minutes before serving.