(Begin about 1 hour and 20 minutes ahead of serving time; it should be served warm.)
Preheat oven to 350° F.
Drain pineapple, reserving 2 tablespoons of the syrup.
Melt butter in a 10-inch heavy skillet, over low heat. Add brown sugar, stirring until sugar is melted. Remove from heat. Arrange drained pineapple on sugar mixture in skillet. Fill centers of pineapple slices with cherries and spaces between slices with pecans. Set aside.
Into medium bowl, sift flour with granulated sugar, baking powder, and salt. Add shortening and milk. With electric mixer at medium speed, beat for 2 minutes. (Easy to mix by hand actually.)
Add egg and reserved pineapple syrup; beat 2 minutes longer. Pour cake batter over pineapple in skillet, spreading evenly.
Bake 40 to 45 minutes, or until cake springs back when gently pressed with fingertip.
Let stand on a wire rack just 5 minutes. Loosen cake from edge of skillet. Cover with serving plate; invert; shake gently, then lift off pan.
Serve warm with whipped cream.