Defrost puff pastry and using a rolling pin, roll out the pastry until smooth and a bit larger than the size of a 9-10 inch cast iron skillet. Refrigerate puff pastry until ready to use.
Preheat oven to 375 degrees F.
In the cast iron skillet set over medium heat, melt the butter and honey, stirring occasionally. When the butter and honey begin to bubble, allow to cook for 5-8 minutes until thick and a dark caramel color. Add the lemon juice and salt, stir and remove from the heat.
Place the halved figs, cut side down, on top of the caramel. Squeeze the figs tightly together in the pan.
Remove the puff pastry from the fridge and lay it directly on top of the figs and caramel. Tuck the edges of the pastry into the pan and prick with a fork.
Bake the tarte tatin for 30-35 minutes, until pastry is golden brown and puffed up.
Cool the tarte Tatin briefly, for 5-10 minutes. Run a knife around the edge of the pastry to separate it from the pan. Shake the skillet a few times to loosen the figs in the caramel sauce. Place a pie plate over the top of the skillet. Using oven mitts, grip the plate and the skillet and quickly turn them both over so the pie plate is on the bottom and the skillet is on top. Gently lift the skillet away and re-arrange any figs that may not have made it perfectly on to the tarte tatin. Don’t worry, it’s totally normal for that to happen! Scrape any remaining caramel sauce from the pan and drizzle over the tarte tatin.