Start to finish: 1 hour and 40 minutes, plus 2 hours to cool
2 1/2 pounds peaches, peeled, halved, pitted, and cut into 1/2-inch wedges
5 tablespoons peach schnapps
4 teaspoons lemon juice
3 tablespoons granulated sugar
1 cup (5 ounces) all-purpose flour
1 1/4 teaspoons baking powder
3/4 teaspoon salt
1/2 cup packed (3 1/2 ounces) light brown sugar
1/3 cup (2 1/3 ounces) plus 3 tablespoons granulated sugar
2 large eggs, room temperature
8 tablespoons unsalted butter, melted and cooled
1/4 cup sour cream
1 1/2 teaspoons vanilla extract
3/8 teaspoon almond extract
1/3 cup panko bread crumbs, crushed fine
For the peaches: Adjust oven rack to middle position and heat oven to 425 F. Line rimmed baking sheet with aluminum foil and spray with vegetable oil spray. Grease and flour 9-inch springform pan. Gently toss 24 peach wedges with 2 tablespoons schnapps, 2 teaspoons lemon juice, and 1 tablespoon sugar in bowl; set aside.
Cut remaining peach wedges crosswise into 3 chunks and gently toss with remaining 3 tablespoons schnapps, 2 teaspoons lemon juice, and 2 tablespoons sugar in second bowl. Spread peach chunks onto prepared baking sheet and bake until exuded juices begin to thicken and caramelize at edges of pan, 20 to 25 minutes. Let peaches cool completely on pan, about 30 minutes. Reduce oven temperature to 350 F.
For the cake: Whisk flour, baking powder, and salt together in bowl. Whisk brown sugar, 1/3 cup granulated sugar, and eggs in large bowl until thick and thoroughly combined, about 45 seconds. Slowly whisk in melted butter until combined. Whisk in sour cream, vanilla, and 1/4 teaspoon almond extract until combined. Add flour mixture and whisk until just combined.
Pour half of batter into prepared pan and spread to pan edges with rubber spatula. Sprinkle crushed panko over roasted peaches and toss gently to combine. Arrange peaches evenly in pan and press gently into batter. Gently spread remaining batter over peaches, smooth top, and arrange reserved peaches attractively over top, also placing wedges in center. Combine remaining 3 tablespoons granulated sugar and remaining 1/8 teaspoon almond extract in bowl; sprinkle over top.
Bake cake until golden brown and toothpick inserted in center comes out clean, 50 minutes to 1 hour, rotating pan halfway through baking. Let cake cool in pan on wire rack for 5 minutes. Run thin knife around edge of pan to loosen cake, then remove sides of pan. Let cake cool completely on rack, 2 to 3 hours. Slide thin metal spatula between cake bottom and pan bottom to loosen, then slide cake onto platter. Serve.
Nutrition information per serving: 270 calories; 99 calories from fat; 11 g fat (7 g saturated; 0 g trans fats); 70 mg cholesterol; 268 mg sodium; 37 g carbohydrate; 1 g fiber; 25 g sugar; 3 g protein.