Mix flour, sugar, and salt in a food processor.

Cut in chilled butter until the mixture resembles coarse meal.

Mix ice water and cider vinegar in a small bowl.

Add the liquid mixture to the processor and blend until moist clumps form.

Add more ice water if the dough is dry.

Gather the dough into a ball, flatten into a disk, wrap in plastic, and refrigerate for at least 1 hour.

Fill a large skillet with ice cubes.

Combine sugar, water, and honey in a heavy ovenproof skillet.

Stir over medium heat until sugar dissolves.

Increase heat to medium-high and boil until the caramel is deep amber, occasionally brushing down the sides with a wet pastry brush.

Swirl the skillet, about 8 minutes.

Remove from heat and stir in butter and cinnamon.

Immediately place the skillet with caramel atop ice in the large skillet.

Let stand until caramel is cold and hardened, about 30 minutes.

Remove the skillet from the ice.

Position the rack in the center of the oven; preheat to 400°F.

Arrange quince wedges tightly together, rounded side down, in concentric circles atop caramel in the skillet.

Fill the center with any broken quince pieces.

Roll out the dough on a lightly floured surface to a 12 1/2-inch round.

Place the dough atop the quinces and tuck the edges down around the sides.

Make three 2-inch-long cuts in the center of the dough to allow steam to escape during baking.

Place the skillet on a rimmed baking sheet.

Bake until the quinces are tender and the crust is deep golden brown, about 1 hour 15 minutes.

Remove from oven and let cool for 30 minutes.

Place a large platter atop the skillet.

Using oven mitts, hold the platter and skillet firmly together and invert, allowing the tart to slide out onto the platter.

Rearrange any dislodged quince wedges, if necessary.

Serve warm or at room temperature.