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1
Make cake: Put oven rack in middle position and preheat oven to 350F Butter 2 (8- by 2-inch) round cake pans and dust with flour, knocking out excess.
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2
Whisk together flour (1 1/2 cups), baking powder, cinnamon, salt, nutmeg, cloves, and allspice in a medium bowl.
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3
Combine apple cider and lemon juice in a small measuring cup.
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4
Beat butter in a large bowl with an electric mixer at medium-high speed until light and fluffy, then add brown sugar and beat until combined.
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5
Add eggs 1 at a time, beating well after each addition (mixture will look curdled).
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6
Reduce speed to low and add flour mixture and cider mixture alternately in 3 batches, beginning and ending with flour mixture and mixing until just combined.
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7
Divide batter between cake pans (batter will form a thin layer) and rap pans on work surface once to release any large air bubbles.
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8
Bake cake layers until they begin to pull away from sides of pans and a wooden pick or skewer inserted in center of each cake layer comes out clean, 25 to 30 minutes.
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9
Cool cake layers in pans on racks 5 minutes, then run a thin knife around edge of each layer and invert layers onto racks.
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10
Cool completely, at least 1 hour.
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11
Make buttercream while cakes cool: Whisk together sugar, cornstarch, and salt in a 2-quart heavy saucepan.
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12
Whisk in cider, then bring to a boil over moderate heat, whisking constantly, and boil, whisking constantly, 1 minute (mixture will be very thick).
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13
Transfer to a metal bowl and set in a larger bowl of ice and cold water, then stir occasionally until cool, about 30 minutes.
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14
Beat butter in a large bowl with cleaned beaters at medium-high speed until light and fluffy, then add one third of cider mixture and beat until incorporated.
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15
Add remaining cider mixture and continue beating until smooth.
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16
When cakes are cool, arrange 1 layer flat side up on a flat serving plate or cake stand and spread top with 3/4 cup buttercream.
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17
Top with remaining cake layer flat side up.
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18
Frost top and side of cake with remaining buttercream.
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19
Chill 2 hours before serving (to firm up buttercream).
