Doughnuts and doughnut holes made with cornmeal and rich pumpkin puree are in keeping with the season. Roll some in confectioners' sugar and others in a mixture of cinnamon and sugar. A tall glass of apple cider is the perfect accompaniment.
Sift flour, baking powder, salt, 1/2 teaspoon cinnamon, and allspice together into a large bowl. Add orange zest and cornmeal; mix until combined. Set aside.
In an electric mixer fitted with the paddle attachment, beat the eggs and 1/4 cup granulated sugar until the mixture is pale yellow, about 5 minutes. Add condensed milk, and beat well. Add the pumpkin and melted butter, and beat until combined. Add the reserved flour mixture, and mix until the dough holds together. Cover the dough with plastic wrap, and refrigerate overnight.
Heat the vegetable oil in a large deep pan over medium heat until a deep-frying thermometer reads 365 degrees.
While oil is heating, roll out the dough on a lightly floured surface to about 1/3 inch thick. Using a 3-inch doughnut cutter, cut out doughnuts, and set aside. Reroll scraps of dough, and continue to cut out more doughnuts. Mix together remaining 1/2 teaspoon cinnamon and 1/4 cup sugar in a small bowl, and set aside.
Add 4 doughnuts to hot oil; fry until golden brown, about 1 1/2 minutes. Turn doughnuts over; fry until golden brown, about 1 minute more. Transfer doughnuts to several layers of paper towels to drain. Repeat until all doughnuts have been fried.
Roll half the warm doughnuts, one at a time, in cinnamon sugar to coat. Transfer to a serving platter. Dust remaining doughnuts with confectioners' sugar. Transfer to the serving platter. Serve warm.
If you do not have a doughnut cutter, use a three-inch cookie cutter to cut out the doughnuts and a one-inch cookie cutter to cut out the center of each doughnut.