Preheat oven to 350°F. Butter an 8" or 9" round cake pan and put the brown sugar, butter and maple syrup in it - put it into the oven as it preheats and then stir with a fork until smooth and scatter with the berries.
In a largish bowl, beat the butter and sugar for a few minutes, until pale and fluffy. Beat in the egg and vanilla. In a small bowl, stir together the flour, baking powder, baking soda and salt.
By hand or with the mixer on low speed, add the flour mixture in 3 batches, alternating with buttermilk, beginning and ending with flour, mixing each time just until combined. Spread the batter over the blueberries the pan, smoothing the top.
Bake for 25-30 minutes, until golden and springy to the touch.
Let cool for 10 minutes, then invert onto a cooling rack or plate, or eat warm, straight from the pan.