In a large bowl, mix together flour, sugar, salt and sage for the dough. Using your hands, mix in half of the butter, squeezing the cubes between your fingers, until the mixture resembles a coarse meal. Add in the remaining butter, squeezing the cubes between your fingers once again, until the largest pieces of butter are approximately the size of a pea.
Drizzle water over the dough and bring together, kneading 3 to 4 times. Flatten the dough into a disk, wrap tightly in plastic wrap and cool in the refrigerator for 30 minutes.
While the dough is chilling, heat a small skillet with olive oil for the filling over medium-high heat. Once the pan is hot, add the sliced onion for the filling. Cook until the onions are tender. Add in the water and continue to cook down until the onions are caramelized and brown. Remove from heat and set aside.
When ready to bake, preheat oven to 375 degrees. Line a rimmed baking sheet with parchment paper.
Roll out the galette dough into a 10” round.
Leaving a 1 1/2 to 2-inch border, add 3/4 of the asiago cheese. Top with sweet potato slices, caramelized onion and the remaining cheese.
Fold the pastry edge up and over the filling to create a 1” border. Brush the pastry border and edges with the melted butter.
Bake for 35 minutes. Transfer the galette with the parchment paper onto a rack to cool for approximately 5 minutes before serving.
While the galette is baking, make the white wine reduction. In a small saucepan over medium-high heat, heat the olive oil. Add onion and garlic and cook until tender, approximately 5 minutes. Stir in oregano, thyme, white wine and orange juice. Bring to a boil and cook, stirring occasionally, until reduced by half, approximately 2-3 minutes. Remove from heat and stir in the butter until melted.
Garnish galette with a sprinkle of fresh sage and serve with the white wine reduction.