Combine heavy cream, chicken broth, and bay leaf in a large saucepan; season with salt and pepper. Add cardoon pieces. Bring mixture to a boil; reduce heat and simmer until cardoon is soft, about 1 hour.
Transfer cardoon pieces to a 9x13-inch baking dish with a slotted spoon.
Preheat oven to 350 degrees F (175 degrees C).
Simmer cream mixture until reduced to 3/4 cup, 5 to 10 minutes. Pour cream over cardoon pieces in the baking dish. Sprinkle Gruyere cheese on top.
Bake in the preheated oven until top is browned, about 30 minutes.