Atlantic halibutrests in a broth of fresh herbs with tinycockles, cooked justuntil theyopen wide.
Cover mushrooms with boiling water. Let stand until softened, about 3 minutes. Drain, and finely chop; set aside.
Put 1/4 cup of each of the herbs into a food processor; set aside. Stir together remaining 3 tablespoons of each of the herbs, the mushrooms, oil, and 1/2 teaspoon salt in a medium bowl; set aside.
Bring stock to a boil in a medium pot. Reduce heat to medium-low; add cockles. Cover; cook until cockles open, about 2 minutes. Discard any that do not open. Using a slotted spoon, transfer cockles to a bowl, and cover. (Keep heat on).
Season both sides of fish with salt and pepper. Add to stock. Cover; cook, carefully turning once, until center is opaque, 2 to 3 minutes per side. Using a slotted spatula, transfer fish to a plate, and cover.
Bring stock to a boil. Pour half the stock into food processor with herbs; puree (be very careful with hot liquid). Add to remaining stock; pour through a fine sieve into a medium bowl, pressing on herbs; discard herbs. Divide fish and cockles among bowls. Ladle broth into bowls; top fish with reserved herb mixture.