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1
Make the cake:.
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2
Position a rack in the center of the oven and heat the oven to 325F Butter and flour a 10-cup Bundt pan; tap out excess flour.
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3
In a large bowl with a hand mixer or in a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until well combined, about 1 minute.
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4
Add the oil and beat until combined, about 15 seconds.
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5
Add the eggs one at a time, mixing well on low speed.
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6
Add the vinegar and vanilla and mix again until just combined.
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7
Add half of the flour and the baking soda, salt, ginger, and nutmeg, mixing on low speed until just combined.
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8
Add half of the buttermilk and mix until just combined.
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9
Repeat with the remaining flour and buttermilk.
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10
Stir the squash into the batter and transfer the batter to the prepared pan; smooth the top with a rubber spatula.
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11
Bake until a cake tester inserted in the center comes out clean, about 1 hour.
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12
Cool on a wire rack for 30 minutes; then carefully invert the cake onto the rack and remove the pan.
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13
When the cake is completely cool, transfer it to a serving plate.
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14
Make the icing:.
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15
In a medium bowl, whisk the sugar, buttermilk, vanilla, nutmeg, and salt until smooth.
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16
Add more buttermilk, a few drops at a time, as needed, until the icing is pourable but still quite thick.
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17
Pour the icing back and forth in thick ribbons over the cooled cake.
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18
Sprinkle the ginger on top.
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19
Let the icing set at roomtemperature, about 45 minutes, before serving.
