Preheat the oven to 350 degrees F. Lightly oil or butter a baking dish or casserole.
In the baking dish, stir together the hominy and corn leveling off the top of the mixture with a rubber spatula. Top with the garlic and cheddar.
Whisk together the milk, eggs, salt, and cayenne in medium bowl, and pour this mixture over the top. Bake for 50 to 60 minutes, or until the casserole is set and the top is bubbling. Remove from the oven, let rest for 5 to 10 minutes, and serve hot.