Preheat oven to 350°.
Place butter in a 9-inch round cake pan; place in oven 2 minutes or until butter melts. Remove pan from oven.
Sprinkle brown sugar evenly over bottom of pan. Arrange pear slices and pecan halves spoke-like over sugar; set aside.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, baking powder, baking soda, and salt in a medium bowl. Beat sugar, butter, egg, and extracts with a mixer at medium speed until well blended. Add sour cream and half of flour mixture; beat well. Add remaining flour mixture and milk; beat well. Pour batter over pear slices, spreading gently. Bake at 350° for 30 to 33 minutes or until a wooden pick inserted in center comes out clean. Cool on a wire rack 5 minutes.
Run a sharp knife around edge of pan to loosen cake. Place a serving plate upside-down over pan; invert cake onto serving plate. Serve warm or cool completely.