Heat oven to 400°F. Use a 10-inch oven-safe skillet.
Peel, halve, and core the pears. Pat the cut sides dry.
Melt butter with maple syrup and brown sugar in the skillet over medium heat. Simmer until glossy and slightly thick, 3–4 minutes.
Stir in lemon juice, vanilla, cinnamon, and salt. Reduce heat to medium-low.
Nestle pears cut-side up into the caramel. Spoon sauce over and cook until just tender at the edges, 8–10 minutes.
Lightly flour your surface. Roll the puff pastry into a round slightly larger than the skillet.
Lay pastry over the pears. Tuck edges down around the fruit and cut a few small vents.
Bake until the pastry is deep golden and the caramel bubbles at the edges, 25–30 minutes.
Cool 5 minutes. Invert onto a plate, letting the caramel coat the pears. Slice and serve warm.