PREPARE THE TOPPING

1. Position a rack in the center of the oven and preheat to 350°F. Grease the bottom and sides of a 10 × 3-inch round cake pan (don’t use a springform pan, or the caramel might leak out during baking). Line the bottom of the pan with a round of parchment paper and grease the paper.

2. In a medium saucepan, combine the sugar and water, and cook over medium heat, stirring until the sugar dissolves. Stop stirring; increase the heat to high, and cook, occasionally brushing down the sides of the pan with a wet pastry brush to prevent crystallization, until the mixture turns into a golden caramel. Remove the pan from the heat and immediately whisk in the butter, one piece at a time (be careful—the mixture will bubble up furiously). Carefully pour the hot caramel into the bottom of the prepared pan.

3. Cut the peaches in half and discard the pits. Cut each peach half into 6 wedges. Arrange a circle of wedges, overlapping them slightly, around the edge of the pan, on top of the caramel. Arrange another circle of wedges in the center, facing the opposite direction, covering the caramel completely.

MAKE THE CAKE

4. Sift together the flour, baking powder, baking soda, cinnamon, ginger, and salt into a medium bowl. Whisk to combine, and set aside.

5. In a small bowl, stir together the sour cream and vanilla extract; set aside.

6. In the bowl of an electric mixer, using the paddle attachment, beat the butter at medium-high speed until creamy, about 1 minute. Gradually add the sugar and beat at high speed until the mixture is lightened in texture and color, 2 to 3 minutes. Reduce the speed to medium and add the eggs one at a time, beating well after each addition and scraping down the sides of the bowl as needed. At low speed, add the flour mixture in three additions, alternating it with the sour cream mixture in two additions and mixing just until blended.

7. Spoon the batter in large dollops over the peaches, then smooth it into an even layer. Bake for 45 to 50 minutes, until the cake is golden brown and springs back when lightly touched. Set the pan on a wire rack and cool for 10 minutes.

8. Run a thin-bladed knife around the edge of the pan. Using pot holders, very carefully invert the cake onto a cake plate or platter. Peel off the parchment paper if necessary. Serve the cake warm or at room temperature.