Melt butter in skillet over moderate heat until foam subsides. Reduce heat to low, then sprinkle brown sugar over bottom of skillet and cook, undisturbed, 3 minutes (not all sugar will be melted). Arrange pears decoratively over sugar and cook, undisturbed, 2 minutes.
Remove from heat.
Preheat oven to 350°F.
Whisk together flour, baking soda, cinnamon, ginger, cloves, and salt in a bowl.
Whisk together molasses and boiling water in a small bowl. Beat together butter, brown sugar, and egg in a large bowl with an electric mixer at medium speed until creamy, about 2 minutes, then alternately mix in flour mixture and molasses in 3 batches at low speed until smooth.
Pour batter over topping in skillet, spreading evenly and being careful not to disturb pears, and bake in middle of oven until a tester comes out clean, 40 to 50 minutes.
Cool cake in skillet on a rack 5 minutes. Run a thin knife around edge of skillet, then invert a large plate with a lip over skillet and, using pot holders to hold skillet and plate tightly together, invert cake onto plate. Replace any pears that stick to skillet.