Preheat the oven to 350ºF (180ºC) and grease an 8-inch (20 cm) square baking dish with the butter. Set aside.
Whisk the flour, sugar, baking powder, cinnamon, and salt in a mixing bowl.
In a smaller bowl, whisk the oil, eggs, and vanilla until smooth.
Make a well in the dry ingredients and pour in the egg mixture. Fold together until all dry bits of flour are just mixed in.
Spoon the batter into the prepared baking dish, smooth the top, and scatter the blueberries evenly over the surface. Sprinkle with coarse sugar if using.
Bake for 40 to 45 minutes, or until the edges are golden and the middle is set. Transfer to a wire rack to cool before slicing and serving.
Notes
For accuracy, I highly recommend using a digital kitchen scale and an oven thermometer.
Fold the batter gently just until you no longer see dry flour. A few streaks are ok.
The full amount of blueberries may look like a lot, but they settle as the cake bakes.
Don't skip the coarse sugar sprinkle if you don't have to. It gives the cake a subtle sparkle and a light, sweet crunch. I get mine at Bulk Barn (not sponsored).
Storage
Once cooled, cover the cake tightly and store it at room temperature for up to 2 days. If your kitchen is warm, store it in the refrigerator instead, but let it come to room temperature before serving.
This cake freezes well. I like to wrap individual slices and store them in an airtight container or zipper-top freezer bag for up to a month.