Preheat oven to 350 degrees F (175 degrees C).

Place onions into a food processor and pulse a few times to coarsely chop. Transfer onions to a large bowl. Place carrot into food processor and pulse once or twice to chop; process until very finely chopped, about 30 seconds. Add carrot to onions. Place whitefish fillets into food processor and grind until the fish is a fine paste, about 2 minutes. Add fish to bowl.

Combine onions, carrot, and whitefish with cold water, matzo meal, egg, egg whites, sugar, vegetable oil, nutmeg, salt, and black pepper, stirring to combine well. Spoon whitefish mixture into 16 muffin cups, filling them level with the top edge.

Bake in the preheated oven until gefilte fish cakes are set and a toothpick inserted into the center of a cake comes out clean, about 1 hour. Let cool in muffin cups, remove, cover, and refrigerate until chilled, at least 1 hour.