For the peaches: Adjust oven rack to middle position and heat oven to 350 degrees. Grease 9-inch springform pan. Combine sugar and cinnamon in medium bowl; reserve 2 tablespoons sugar mixture. Add peaches to bowl with remaining sugar mixture and toss to coat.
For the cake: Whisk flour, baking powder, and salt in bowl. With electric mixer on medium-high speed, beat sugars and butter until light and fluffy, about 2 minutes. Beat in eggs, sour cream, and vanilla until incorporated.
Reduce speed to medium-low. Slowly add flour mixture and mix until just combined, about 30 seconds. Scrape batter into prepared pan. Scatter dried peaches over batter, then arrange sugared peaches in circular pattern over top, reserving 3 slices to fill the middle. Sprinkle reserved sugar mixture over peaches.
Bake until cake is golden brown and toothpick inserted in center comes out clean, 35 to 45 minutes. Cool at least 1 hour.
Note: Cake can be stored at room temperature, wrapped in plastic, for 2 days.