Add the sweet potatoes to a large pot, cover with water and add 1 tablespoon salt. Bring to a boil over medium-high heat and cook until the potatoes are easily pierced with a knife, 10 to 15 minutes. Drain and puree the potatoes in a food processor until smooth.
Bring the heavy cream and 2 cups water to a simmer in a saucepan over medium heat. Slowly whisk in the polenta and garlic powder. Reduce the heat to low and continue to cook, stirring occasionally, until the polenta is smooth and cooked through, about 15 minutes. Stir in the sweet potato puree and cheese until well combined. Season with salt and pepper.