Place the corncobs and water in a large stockpot or dutch oven over high heat. Bring to a boil, turn the heat to low, and let simmer for 2–3 hours. Use tongs to pull cobs from the broth and place them in a colander set over a bowl to catch the liquid. Once they have cooled to room temperature, squeeze cobs into the broth to capture the last bits of flavor, then discard them.

Heat olive oil in a large saucepan over medium heat. Add shallot and garlic and sweat until translucent (about 5 minutes), lowering heat if necessary to avoid browning the shallots.

Add corn kernels and cook for another 5 minutes, stirring occasionally. Add corn stock and bring to a low simmer for about 10 minutes.

Pour soup into a blender; blend until smooth. Pass soup through a strainer. Add heavy cream, if using. Chill in the refrigerator or an ice bath until the soup is cold. Garnish with zhoug, cotija, and heirloom cherry tomatoes.