Preheat the oven to 400°. Arrange the garlic cloves and the whole sage leaf on a piece of foil and drizzle with 1 teaspoon of the olive oil. Wrap up the garlic in the foil and roast for about 40 minutes, until the cloves are very soft. Let cool, then peel the garlic.
Meanwhile, spread the walnuts in a pie plate and toast for about 5 minutes, until golden brown. Let the walnuts cool, then coarsely chop them.
In a medium saucepan, cover the squash with water. Bring to a boil and simmer over moderate heat until tender, about 15 minutes. Drain well and transfer to a bowl. Add the roasted garlic and the sage leaf to the squash and mash with a fork.
In a large nonstick skillet, heat 1 tablespoon of the olive oil. Add the shallot and minced sage and cook over moderate heat until the shallot is softened, 3 minutes. Mix the shallot and sage into the mashed squash and season with salt and pepper. Wipe out the skillet.
Working with 4 wonton wrappers at a time, mound a rounded teaspoon of squash filling in the center of each wrapper. Brush the edges of the wrappers with water and fold each one into a triangle, pressing the edges to seal. Bring the pointed edges together and press to seal. Transfer the stuffed wontons to a baking sheet and cover them with plastic wrap. Repeat with the remaining wonton wrappers and filling.
Oil a steamer basket and set it over simmering water. Arrange half of the wontons in the basket, cover and steam for 5 minutes. Transfer the steamed wontons to a large plate. Repeat with the remaining wontons.
Heat the remaining 1 tablespoon of olive oil until shimmering. Add the wontons and cook over moderate heat, turning once, until lightly browned and crisp, 2 minutes per side. Transfer the wontons to a platter, sprinkle with the toasted walnuts and cheese and serve.