1. Heat oil in a large skillet over medium-high heat. Add onions and cook, stirring occasionally, until starting to brown (6 minutes). Reduce heat to low, cover and cook, stirring occasionally, until very soft and caramelized (10-60 minutes).
2. Use the vinegar to deglaze the pan. Stir in sage and pepper.
3. Place oven rack in the lowest position; preheat to 450 degrees F. Coat a large baking sheet with cooking spray.
4. Roll out dough on a lightly floured surface to the size of the baking sheet. Transfer to the baking sheet. Bake until puffed and lightly crisped on the bottom (8-10 minutes).
5. Toast walnuts in a small dry skillet over medium-low heat, stirring, until lightly browned and fragrant (2-3 minutes).
6. Spread onions on the crust and top with pears, walnuts, and cheese. Bake until the crust is crispy and golden and the cheese is melted (11-13 minutes). Slice and serve.