I presume carp soup is soup made from the fish called carp.
The descriptive word in salads, soups &c is singular.
Onion pie, potato salad, leek soup, carrot cake, nut loaf, fish soup, carp soup, steak and kidney pudding, bread and butter pudding, &c.
Three onion pies, 4 potato salads, 10 carrot cakes, &c.
It's also singular in expressions such as three cheese sauce, even though three different cheeses are used.