Line an 8-inch by 4 1/4-inch loaf pan with parchment paper. Move the oven rack to the middle position and preheat it to 350 degrees F.
Weight the flour, baking powder, baking soda and salt into a bowl and whisk together to combine.
Whisk together the yogurt, eggs and vanilla extract until smooth and runny.
In the bowl of an electric mixer add the room temperature unsalted butter and sugar and beat until light in color and fluffy (about 5 minutes).
Add the 1/3 of the flour mixture and mix until just combined. Add 1/2 of the yogurt mixture and mix until just combined. Add another 1/3 of the flour mixture and mix until just combined. Add the rest of the yogurt mixture and mix until just combined. Add the remaining flour and mix until just combined.
Toss the blueberries with a tablespoon of flour, which will help them incorporate with the batter better.
Add the blueberries to the batter and fold them in with a spatula by hand.
Scoop the batter into the prepared loaf pan and flatten off the top, making sure the batter goes all the way to the corners.
Bake the blueberry cake until a toothpick inserted into the center comes out clean (about 50-55 minutes).
Remove the cake from the oven and let it cool for 10 minutes.
Spoon the maple syrup evenly over the cake, waiting till each pour gets absorbed into the cake before pouring on more.
Let the cake cool in the pan and then cover the pan with foil and let the cake rest overnight for the syrup to seep evenly into the cake.