How to Make It
Preheat oven to 425°F. Poke holes all over sweet potatoes with a fork; drizzle with 1 tablespoon of the oil, and rub to evenly coat. Place potatoes on a rimmed baking sheet.
Cut and discard about ¼ inch off the top of garlic head to expose garlic cloves; place garlic head on a large piece of aluminum foil. Drizzle with 1 tablespoon of the oil; season with ⅛ teaspoon of the salt and several grinds black pepper. Wrap foil around garlic head to seal, and place on baking sheet with potatoes. Bake in preheated oven until potatoes are tender when squeezed, 40 to 45 minutes.
Cut potatoes lengthwise; scoop out the flesh with a spoon, and transfer to a bowl. Discard skins. Unwrap garlic head, and squeeze cloves from skins into bowl with potatoes. Discard skins. Mash potatoes and garlic using a potato masher or fork. Set aside.
Heat remaining 2 tablespoons oil in a small skillet over medium-high. Add sage leaves, and fry until crispy, about 10 seconds. Remove sage leaves with a slotted spoon, and drain on a plate lined with paper towels; season with ⅛ teaspoon of the salt. Reserve sage oil in skillet.
Bring water and 1 teaspoon of the salt to a boil in a large saucepan over medium-high. Gradually whisk in polenta; reduce heat to medium-low, and cook, stirring constantly, until polenta is tender and mixture is thickened, about 5 minutes. Fold in potato mixture, reserved sage oil, remaining 1 teaspoon salt, and several grinds black pepper. Top with fried sage leaves.