Pit and slice the peaches into 6-8 thick wedges, about 1.5cm (1/2 inch) wide, setting them aside in a single layer. Lightly flour a work surface and roll the puff pastry just enough to smooth out fold lines. Using the skillet as a guide, cut the pastry into a circle about 2.5cm (1 inch) wider than the skillet's rim and refrigerate.
Preheat the oven to 190°C (375°F). Melt the butter in the 25cm (10-inch) oven-safe skillet over medium heat. Add the sugar and salt, stirring once or twice to combine, then stop stirring. Let cook undisturbed, swirling the pan occasionally, until it turns a deep amber color, about 8 to 10 minutes.
Remove the skillet from the heat and carefully stir in the lemon juice, standing back as it bubbles. Arrange the peach wedges in the caramel, rounded side down, packing them tightly in a circular pattern. Return to medium heat and cook for 5 to 7 minutes, until the peaches soften slightly at the edges but still hold their shape.
Lay the chilled pastry circle directly over the peaches. Tuck the edges down into the gap between the fruit and the skillet using a spoon or offset spatula. Cut 3 to 4 small slits in the top of the pastry to let steam escape.
Transfer the skillet to the oven and bake for 25 to 30 minutes, until the pastry is deeply golden brown and puffed. Check at the 20-minute mark; if the pastry is browning too quickly, loosely tent it with foil for the remaining time. Remove once the crust looks crisp and the caramel is bubbling visibly at the edges.
Let the tarte tatin rest in the skillet on a wire cooling rack for 8 to 10 minutes. Place a large serving plate upside down over the skillet. Using oven mitts, hold the plate and skillet firmly together and flip both in one confident motion. Lift the skillet away slowly, scraping any caramel left in the pan back over the top of the tart.