For topping: Preheat oven to 350°F Melt 1/4 cup butter in 10-inch-diameter cast-iron skillet or other heavy ovenproof skillet (preferably nonstick) over medium heat. Add 2/3 cup brown sugar and stir until mixture begins to form thick mass, about 4 minutes. Continue cooking, without stirring, until butter mixture spreads and covers bottom of skillet and bubbles appear all over surface, about 6 minutes longer. Remove skillet from heat. Arrange pineapple chunks close together in concentric circles atop sugar mixture in skillet.
For cake: Sift first 8 ingredients into medium bowl. Using electric mixer, beat molasses, golden brown sugar, melted butter, eggs and vanilla extract in large bowl until well blended, about 2 minutes.
Add half of dry ingredients, then whole milk, then remaining half of dry ingredients, beating until well blended after each addition.
Beat in crystallized ginger. Spread batter evenly over pineapple in skillet.
Bake cake until tester inserted into center comes out clean, about 40 minutes.
Cool cake in skillet 5 minutes. Run small knife around sides of skillet to loosen cake.
Place platter over cake in skillet; invert cake onto platter. Cool cake at least 1 hour. Serve slightly warm or at room temperature with whipped cream.