Use 9x3 springform pan or 9 inch round cake pan.
Preheat oven to 375°F with rack in middle. Line the bottom of a 9x3-inch springform pan (or 9 inch round cake pan) with parchment paper. Grease the side of the pan with butter or cooking spray.
Sift flour, baking powder, baking soda, and salt together into a medium bowl.
In a separate bowl, beat butter and sugar until light and fluffy. Add vanilla and egg and continue beating until very creamy and light in color.
Keeping the mixer speed low, mix in the flour in 2 batches, adding ½ cup Greek yogurt in between the 2 batches to the cake batter until combined. Do not overmix.
Transfer the cake batter to the springform pan. Scatter blueberries evenly on top.
Bake until cake turns golden, and the tester comes out clean, about 20 to 35 minutes, depending on your oven.
When the cake is done baking, let it cool (still in the baking pan) on a wire rack. After cake has cooled for about 40 minutes, release the cake from the springform pan. At this point, if the cake is cool enough, you can slide your hand under the cake, between the parchment paper and the bottom portion of the springform pan and move the cake with the parchment paper attached to its bottom onto a cake plate easily.
If using a 9 inch round cake pan, cook in pan for about 30-40 minutes, then invert onto a plate.