¼lbunsalted butter (1 stick, 114g) plus more for greasing the pan
1¼cupgranulated sugar (250g) – divided
1cupall-purpose flour (120g)
Heat oven to 350 degrees. Butter a 10-inch pie pan. Line the bottom of the pan with a round of parchment paper and butter that as well. Pit the peaches and cut into slices about 1/2-inch thick, then arrange the slices on the bottom of the pie pan.
Make caramel: Put 1/2 cup/100 grams of the sugar in a small skillet or saucepan. Cover it with 1/4 cup/60 milliliters of water. Bring it to a simmer over medium heat, and make sure the sugar is dissolved – this takes about 5 minutes. Increase the heat to medium-high and cook without stirring until the mixture turns amber, about 5 minutes more. Remove from heat immediately and pour this caramel evenly over the peaches in the pie pan.
Make cake batter: In a medium bowl, sift together the flour, baking powder and cardamom, and set aside. In another medium bowl, beat together the butter and remaining 3/4 cup/150 grams sugar until light and fluffy. Beat in the eggs 1 at a time, then stir in the flour mixture. Spread the batter evenly over the peaches and caramel.
Bake for 30 to 35 minutes, until top is golden brown and cake is set. Remove from the oven and set on a cooling rack, and cool about 10 minutes. Run a knife around the sides to loosen the cake, then position a platter on top and invert the cake onto the platter. Lift off the parchment (the caramel will still be very hot!) If any of the peach slices stick to the parchment, lift them off carefully and replace them on top of the cake.
Serve the cake warm or cooled to room temperature.
Adapted from Florence Fabricant's recipe published in the New York Times.