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Preheat oven to 350°F.
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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.
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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.
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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. Serve warm or at room temperature.