Preheat oven to 350º.
Combine the almonds and powdered sugar in a food processor; pulse 8 times or until finely chopped.
Heat corn syrup and 1 tablespoon butter in a 10-inch cast-iron skillet over medium heat until butter melts. Stir in brown sugar, and cook 1 minute or until bubbly. Remove from heat. Arrange pear slices spokelike in pan, working from center of pan to edge; sprinkle with cherries. Cook over medium heat 15 minutes or until syrupy, gently shaking pan occasionally (do not stir).
While pears cook, place granulated sugar and 1/3 cup butter in a large bowl; beat with a mixer at medium speed 4 minutes or until well blended. Add eggs, 1 at a time, beating well after each addition. Lightly spoon flour into a dry measuring cup; level with a knife. Combine almond mixture, flour, baking powder, and salt, stirring well with a whisk. Add flour mixture and buttermilk alternately to egg mixture, beginning and ending with flour mixture; stir with a rubber spatula just until blended. Stir in extracts. Gently spoon batter over pears, spreading evenly. Bake at 350º for 30 minutes or until golden brown. Run a sharp knife around edge of pan to loosen cake. Place a plate upside down on top of pan; carefully invert cake onto the plate.