Preheat oven to 350 °F. Coat a 9-inch round cake pan with cooking spray.
Toss peaches, brown sugar, 1 tablespoon bourbon (if using) and cornstarch in a bowl. Spoon the fruit into the prepared pan, arranging it in an even layer; set aside.
Combine flour, pecans, baking powder and salt in a food processor; process until the pecans are ground to a fine meal.
Beat 2 egg whites in a mixing bowl with an electric mixer until soft peaks form. Gradually beat in 1/3 cup sugar, continuing to beat until the egg whites are stiff and glossy; set aside. Beat whole eggs with the remaining 1/3 cup sugar in another mixing bowl until thick and pale, about 5 minutes. Beat in the remaining 1 tablespoon of bourbon (if using) and vanilla. Whisk one-fourth of the reserved beaten egg whites into the whole-egg mixture. Sprinkle half of the flour mixture over the top and fold in with a rubber spatula just until blended. Fold in the remaining beaten whites, then the remaining flour mixture.
Spread the batter over the fruit in the pan. Bake until the top springs back when lightly touched and a skewer inserted in the center comes out clean, 35 to 45 minutes. Let cool in the pan for 5 minutes, then invert onto a serving plate, rearranging any stray fruit. Serve warm or at room temperature.
Tips: To peel peaches: Bring a medium saucepan of water to a boil. Immerse peaches in boiling water for 1 minute. Remove with a slotted spoon and plunge into a bowl of ice water to cool slightly. Transfer to a cutting board. Remove the skins with a paring knife.
To toast whole nuts: Spread nuts on a baking sheet and bake at 350°F, stirring once, until fragrant, 7 to 9 minutes.