Heat oven to 400°F (205°C).

Peel your apples. Cut apples in thirds off of the core as best you can (no need for perfectly even thirds) and cut or scoop any remaining seeds out. Squeeze the juice of half a lemon over them and toss to coat.

Have the butter very cold and ready by the stove. Trust me.

Pour sugar into a large (11- to 12-inch) skillet and place over medium-high heat and cook, without stirring, until sugar is partially liquefied, about 4 minutes. Whisk until all unmelted sugar disappears into the caramel and nudge the heat down to medium-low. Cook until the sugar is dark amber, 1 to 2 minutes. Remove from heat, immediately add butter and whisk to melt and combine.

Return to the heat and add the apples and cook over medium-high heat. Cook, gently stirring and turning to ensure even cooking, until apples soften and begin to turn translucent at the edges and are about 3/4 of the way cooked through, about 10 minutes.

Using tongs, transfer apples, rounded side down, one at a time to a smaller (10-inch) skillet with an oven-proof handle or a 10-inch (standard) pie dish. Arrange them in a concentric circle around the outside, overlapping each apple by about 1/3 and purposely crowding them. Arrange remaining apples in the center of the ring.

Pour any extra caramel in the skillet over the apples. Let this cool for 10 minutes, and use this time to roll out the pastry. Roll the dough out to a rough circle about one inch larger than the pan. If you’re not ready to use it yet, chill until needed on a lightly floured plate or tray.

Top sautéed apples with the pastry round, tucking the edges in all around. Cut a vent or two in the center, and place dish or skillet on a baking sheet. Bake for 25 to 30 minutes minutes, or until the pastry is nicely browned and apples are bubbling around the edges.

Run a butter knife around the edges to loosen. Let cool in the pan at least 30 minutes and up to 60 minutes. Peek under the crust if you can, or tilt the pan slightly, looking for evidence that caramel and juices have thickened slightly. To invert, top with a serving plate and grasp the pan and plate tightly together as a unit and flip quickly. Remove the pan. If any apples stick to the pan, just replace them where they should go on the tart. Serve warm, with crème fraîche or whipped cream, if desired.

If it has cooled completely before you serve, either return to the oven (if in a pie dish) or the stove (if in a skillet) to warm up and loosen the caramel for a few minutes. Leftovers keep well in the fridge, rewarm gently before serving.