Dissolve the cornstarch in 1 cup of the milk and set aside. Heat the butter in a large saucepan or soup pot and sauté the onion and garlic until soft and translucent—about 8 to 10 minutes. Add the spices and stir to blend.
Cut the corn off the cobs, then run the back of a knife down the cobs to extract the milk. Add the corn and corn milk to the pot to warm, then carefully transfer the mix to a blender or food processor. While the machine is running, add the reserved cup of dissolved cornstarch and milk. Return the mixture to the pot over medium heat and add the masa harina and remaining milk—stirring occasionally.
Once the soup is heated through, add the green chilies and continue to cook for 10 to 15 minutes. Adjust the salt, if necessary.
To serve, pour the hot soup into ovenproof serving bowls. Top with grated cheese and heat in the oven just long enough to melt the cheese—do not brown. Top with hot sauce and/or pico de gallo, if desired, and serve with tortilla chips.