The pleasure and the reward centers of the brain are control by the neurotransmitter known as dopamine. Besides this, the emotional responses and the movements of a person are also controlled by dopamine.
The reward response from eating ice cream is related to the nucleus accumbens part of the brain. The nucleus accumbens is a part of the basal forebrain, present in each of the brain hemispheres. The dopamine neurons in the VTA (Ventral tegmental area) are activated when the activity such as eating ice cream occurs. These neurons are projected into the nucleus accumbens, and their activation gives a feeling of pleasure.
Hence, the answer is 'nucleus accumbens'.