To make the doughnuts:
Preheat the oven to 400 F.
Grease a standard doughnut pan.
Beat the butter, oil, sugar, salt and spices.
Whisk together the baking powder, baking soda, hi- maize, and flour.
Stir the flour mixture into the wet ingredients alternately with the milk, beginning and ending with flour.
Spoon the batter into the pan, smoothing the tops.
Bake the doughnuts for 10 to 12 minutes, until a cake tester inserted into one cones out clean.
Remove them from the oven, wait 5 minutes, then turn out onto a rack to cool.
To make the glaze: place all the glaze into a saucepan.
Cook over medium heat, stirring frequently, until the sugar is dissolved.
Bring the mixture to a boil, cover the pan, and boil for 3 minutes.
Remove the cover and boil for a few more minutes, until the syrup reaches soft ball stage, 240 F on an instant- read thermometer.
Remove from the heat, and cool slightly.
Carefully dip the doughnuts in the warm syrup; reheat the syrup if it's thickened too much. If you dunk them completely, place them on a piece of greased parchment paper or waxed paper, to set. If you dip just the tops, place them on a rack. Top immediately with chopped nuts or sprinkles, if desired.
Note: any extra syrup will hold for up to a week, covered, in the refrigerator.
Yield: 6 doughnuts