For the cake:

4 oz. (1/2 cup) unsalted butter, softened; more for the pan
13-1/2 oz. (3 cups) unbleached all-purpose flour; more for the pan
1-1/2 cups granulated sugar
1/2 cup canola oil
2 large eggs
1 Tbs. distilled white vinegar
2 tsp. pure vanilla extract
1 tsp. baking soda
1 tsp. table salt
1/2 tsp. ground ginger
1/4 tsp. freshly grated nutmeg
3/4 cup buttermilk
2-1/4 cups peeled and grated butternut squash (about 8 oz.)

For the icing and garnish:

9 oz. (2-1/4 cups) confectioners’ sugar
3 Tbs. buttermilk; more as needed
1 tsp. pure vanilla extract
1/4 tsp. freshly grated nutmeg
1/4 tsp. table salt
1/4 cup finely chopped crystallized ginger