Preheat the oven to 350°F. Coat the interior of an 8½ × 4½ × 2½-inch loaf pan thoroughly with butter or nonstick cooking spray.
Sprinkle a light layer of all-purpose flour inside the greased pan. Tilt the pan to distribute the flour across the bottom and sides, then tap out the excess.
Sift the 1½ cups of all-purpose flour, baking powder, and salt into a large mixing bowl. Place the mixture aside until needed.
In a separate bowl, whisk together the Greek yogurt, granulated sugar, eggs, grated lemon zest, vanilla extract, and vegetable oil. Continue whisking until the ingredients form a smooth, evenly blended mixture.
Room-temperature eggs will incorporate into the batter more readily.
Gradually pour the yogurt mixture into the bowl containing the dry ingredients. Whisk only until the batter is combined and no visible pockets of dry flour remain.
Place the blueberries in a small bowl and toss them carefully with the reserved tablespoon of flour. This light coating helps limit the berries from settling at the bottom of the loaf.
Using a spatula, gently fold the coated blueberries into the batter without crushing them.
Transfer the blueberry batter to the prepared loaf pan and level the surface.
Bake in the preheated oven for approximately 50 minutes, or until a toothpick inserted into the center emerges clean. Depending on the oven, the loaf may require as long as 1 hour 10 minutes.
Begin testing for doneness at the 50-minute point. Rotate the pan halfway through the baking period to encourage an even rise and consistent browning.
While the loaf is in the oven, combine the ⅓ cup lemon juice and 1 tablespoon granulated sugar in a small saucepan.
Warm the mixture over low heat, stirring until the sugar has completely dissolved and the syrup appears clear. Remove it from the heat and set it aside.
After removing the baked loaf from the oven, allow it to rest in the pan for 10 minutes. Carefully turn it out onto a wire rack positioned over a baking sheet.
While the loaf remains warm, use a skewer or toothpick to make small holes across its surface. Slowly spoon or pour the prepared lemon syrup over the loaf, allowing the liquid to penetrate the cake.
Leave the loaf to cool completely before adding the glaze.
Whisk the confectioners’ sugar, ¼ cup lemon juice, and vanilla extract in a small bowl until smooth.
When necessary, add milk in very small amounts until the glaze reaches a fluid but coating consistency.
Drizzle the glaze evenly over the fully cooled loaf. Allow the topping to set before cutting and serving.