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1
Preheat oven to 350u00b0F with rack in middle. Butter and flour cake pans.
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2
Whisk together flour, baking powder, salt, and spices in a large bowl. Stir together milk and vanilla in a small bowl.
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3
Beat butter and sugars with an electric mixer at medium-high speed until pale and fluffy, 3 to 5 minutes. Add eggs 1 at a time, beating well after each addition. At low speed, mix in flour mixture in 3 batches, alternating with milk mixture (begin and end with flour mixture) and mixing until just combined.
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4
Divide batter among pans, smoothing tops, then rap pans once or twice on counter to eliminate any air bubbles. Bake until pale golden and a wooden pick inserted into center of cakes comes out clean, 25 to 30 minutes. Cool in pans on racks 10 minutes. Run a thin knife around edge of pans, then invert cakes onto racks. Reinvert and cool completely.
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5
Peel and core pears, then coarsely chop.
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6
Heat butter in a 12-inch heavy skillet over medium-high heat until foam subsides, then saute pears, stirring occasionally, until just beginning to brown, 2 to 3 minutes. Stir in sugar, lemon juice, and brandy and cook over high heat, stirring, until juices are deep golden and pears are tender, about 5 minutes.
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7
Beat egg whites with cream of tartar and salt using cleaned beaters at medium speed until they just hold soft peaks. Add maple sugar a little at a time, beating, then continue to beat until whites just hold stiff peaks.
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8
Boil maple syrup in a small heavy saucepan over medium heat, undisturbed, until it reaches soft-ball stage (238 to 242u00b0F on candy thermometer), 3 to 7 minutes.
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9
With mixer at low speed, immediately pour hot syrup in a slow stream down side of bowl into egg whites, then beat at high speed, scraping down side of bowl occasionally with a rubber spatula, until meringue is cool to the touch, about 6 minutes. (It's important that meringue be fully cooled before proceeding.)
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10
At medium speed, add butter 1 tablespoon at a time, beating well after each addition. (If buttercream looks soupy after some butter is added, meringue is too warm: Chill bottom of bowl in an ice bath for a few seconds before continuing to beat in remaining butter.) Continue beating until buttercream is smooth. (Mixture may look curdled before all butter is added but will come together before beating is finished.)
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11
Put 1 cake layer on a serving plate, then spread with 3/4 cup buttercream and top with half of pear filling. Top with second cake layer, 3/4 cup buttercream, and remaining pear filling. Top with remaining cake layer, then frost top and sides of cake with remaining buttercream.
