In a medium bowl, stir together the flour, cornmeal, brown sugar, baking powder, baking soda and salt. In a small bowl or measuring cup, stir together the buttermilk and egg.
Stir the wet ingredients into the dry, stirring just until combined. Stir in the blueberries. Heat an inch or two of oil in a heavy, shallow pot (or deep skillet) over medium-high heat until it's hot, but not smoking-a bit of batter or scrap of bread should sizzle if you drop it in, and if you have a thermometer, it should be about 350F.
Drop small spoonfuls of batter into the oil and cook, turning with tongs or a slotted spoon, for 2-3 minutes, or until deep golden. Transfer to a paper towel-lined plate or pan. If you like, stir together the icing sugar and maple syrup, with a little water or milk to thin it further if needed, and drizzle over the fritters while they're still warm. Makes about 2 dozen fritters.