Ginger-Poached Quince Tarte Tatin

Stir together 6 cups water, 2 cups sugar, and ginger in a large pot. Bring to a boil over medium-high; cook, stirring occasionally, until sugar is dissolved, about 5 minutes.

Reduce heat to low, and add quince. Adjust heat as needed to maintain a very gentle simmer, and cook, stirring occasionally, until quince is tender but not mushy and a paring knife slides easily through quince flesh, 25 minutes to 1 hour depending on ripeness and variety of quince. (Check for doneness every 10 minutes after the quince has poached for 25 minutes.) Let quince cool in syrup until warm, about 1 hour.

Preheat oven to 350°F. Roll puff pastry out to 1/8-inch thickness; cut into a 10-inch round; discard scraps. Chill pastry until ready to use. Grease a 9-inch round baking pan with butter; set aside.

Stir together remaining 1/2 cup water and remaining 1 cup sugar in a small saucepan. Bring to a boil over medium-high; boil, undisturbed, until mixture begins to brown around edge of pan, about 10 minutes.

Reduce heat to medium; cook, swirling pan often, until caramel is dark amber and temperature reaches 365°F on a candy thermometer, about 2 minutes. Remove from heat, and whisk in butter and salt. Immediately pour mixture into prepared pan, and swirl pan until bottom is evenly coated in caramel. Set aside.

Drain quince, reserving syrup for another use, if desired. Arrange quince, cut side up, tightly packed in baking pan.

Place pastry over quince, tucking edges into pan so it fits snugly around fruit. Bake in preheated oven until pastry is deep golden brown, 1 hour to 1 hour and 10 minutes. Transfer to a wire rack, and let cool 15 minutes.

Whisk together crème fraîche and cinnamon in a small bowl. Invert quince tart onto a rimmed platter. Serve warm with cinnamon crème fraîche.