In a large bowl, sift together the flour, cornmeal, sugar, baking powder, cinnamon and salt. Set aside.
In another bowl, whisk the beer, eggs, butter, orange zest, orange juice and vanilla. Then stir the liquid ingredients into the dry ingredients, just enough to moisten. Add the apples.
Heat a large saucepan containing 2 inches (5 cm) of oil until an instant-measurement thermometer reads 375 °F (190 °C).
Gently drop 1 tbsp (15 ml) spoonfuls of batter into the hot oil. Fry a few balls at a time until golden brown, about 2 minutes per side.
Using tongs, gently remove the donuts from the oil, drain them on paper towels and sprinkle with icing sugar.
Serve donuts warm, if desired, topped with French vanilla ice cream.
NOTES:
Crunchy and sweet, the Cortland apple retains its shape well when cooked and gives excellent results.