Place squash in a large pot and add enough water to cover; season with salt. Bring water to a boil and cook until squash is tender, about 20 minutes. Drain squash and return to pot.
Mash squash with a potato masher; add evaporated milk, butter, and salt and beat with an electric mixer until smooth and creamy. Stir corn, peas, and Cheddar cheese into squash mixture; cook and stir over medium-low heat until cheese is melted, about 10 minutes. Serve squash mixture over rice.
