Preheat oven to 350°. Spray wells of 2 (6-well) swirled mini-Bundt pans* with cooking spray and sprinkle with cane sugar.

In a large bowl, beat together butter, brown sugar, and granulated sugar with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition.

In a medium bowl, whisk together flour, cinnamon, ginger, baking powder, allspice, baking soda, salt, and nutmeg. In a small bowl, stir together pumpkin, buttermilk, and vanilla extract. With mixer at low speed, gradually add flour mixture to butter mixture alternately with pumpkin mixture, beginning and ending with flour mixture, beating just until combined after each addition. Divide batter among wells of prepared pans, filling three-fourths full. Sprinkle batter with cinnamon sugar.

Bake until a wooden pick inserted near centers comes out clean, 12 to 15 minutes. Let cool in pans for 10 minutes. Turn out cakes onto a wire rack, and let cool completely.

In a large bowl, whisk together confectioners’ sugar and orange juice. Dip top of cakes into glaze, turn over, and let dry on a wire rack.