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1
Bring cream, half-and-half, sage, and zest to a boil in a large heavy saucepan over moderate heat.
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2
Remove from heat and steep, covered, 10 minutes.
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3
Whisk together yolks, granulated sugar, and salt in a large bowl.
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4
Whisk in half of hot cream, then whisk egg mixture into remaining cream in saucepan.
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5
Cook custard over moderate heat, stirring constantly with a wooden spoon, until it coats back of spoon and reaches 170F on thermometer, about 5 minutes (do not let boil).
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6
Pour custard through a fine sieve into a bowl and cool, stirring occasionally.
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7
Chill custard, its surface covered with plastic wrap, until cold, at least 3 hours.
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8
Freeze custard in ice cream maker, then transfer to an airtight container and put in freezer to harden.
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9
Preheat oven to 350F.
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10
Butter a 13- by 9- by 2-inch metal baking pan.
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11
Line bottom with wax or parchment paper, then butter paper.
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12
Sift together flour, cinnamon, allspice, baking soda, and salt.
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13
Whisk together brown sugar and eggs in a large bowl, then whisk in oil and pumpkin puree.
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14
3Add flour mixture and whisk just until smooth.
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15
Pour batter into baking pan and bake in middle of oven until springy to the touch and a tester inserted in center comes out clean, 25 to 30 minutes.
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16
Cool cake in pan on a rack 10 minutes, then run a knife around edge and invert onto rack.
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17
Peel off paper and cool cake completely.
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18
Soak cherries in hot water to cover until softened, about 15 minutes, then drain.
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19
Melt butter in a large skillet over moderate heat.
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20
Add sugars, lemon juice, cinnamon, and salt, then cook, stirring until smooth.
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21
Add pumpkin and drained cherries and simmer, covered, stirring occasionally, until pumpkin is tender, 8 to 12 minutes.
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22
Cut out 12 (3-inch) rounds from cake with cutter.
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23
Halve each round horizontally, then put bottom halves on 12 plates and top with scoops of ice cream.
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24
Spoon compote on and around cakes, then tilt tops against ice cream.
