Melt 1 tablespoon of butter in a large pot set over medium heat. Add the wild rice, garlic, sage and rosemary; cook and stir until the rice is coated and the mixture is fragrant. Pour in 2 cups of the water and bring to a boil. Cover, reduce heat to low and simmer for 10 minutes.
After the 10 minutes, increase the heat to medium and stir in the polenta. Gradually stir in the remaining water as the polenta absorbs it. When all of the water is absorbed, mix in the remaining butter and Cheddar cheese. Reduce heat to low and simmer, stirring frequently for about 20 minutes.
Butter a large baking dish and pour the mixture into it. Spread into an even layer if necessary and set aside to cool and become firm.
When the mixture cools, tap it out onto a cutting board and cut into circles using a large glass or cookie cutter. Grill or fry patties until golden on the outside. Serve with your favorite toppings.
