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1
Preheat oven to 375F.
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2
Peel pears, then halve lengthwise and core.
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3
Spread sugar on a plate, then press cut sides of pear halves into sugar to coat, reserving remaining sugar.
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4
Melt butter in a well-seasoned 10-inch cast-iron skillet over moderate heat until foam subsides.
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5
Reduce heat to low and arrange pears, cut sides down, decoratively in skillet.
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6
Sprinkle reserved sugar all around pears.
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7
Cook pears over moderately low heat until sugar begins to caramelize, about 15 minutes, and remove skillet from heat.
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8
Whisk together flour, baking powder, cardamom, and salt.
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9
Beat together butter and sugar in a bowl with an electric mixer until light and fluffy.
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10
Add vanilla and egg and beat well.
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11
Add flour mixture and milk alternately in 3 batches, mixing at low speed after each addition until just combined.
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12
Spoon batter over pears in skillet, gently spreading evenly and being careful not to disturb pears (batter will not cover tops of all pears).
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13
Bake in middle of oven until golden brown and a tester comes out clean, 20 to 25 minutes.
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14
Cool cake in skillet on a rack 5 minutes.
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15
Run a thin knife around edge and invert a plate over skillet.
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16
Invert cake onto plate (wearing oven mitts), keeping plate and skillet firmly pressed together.
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17
Replace any fruit stuck to bottom of skillet if necessary.
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18
Serve cake warm or at room temperature.
