Preheat oven to 350 degrees F, and adjust rack to the middle position. Butter and flour a 9-by-5-inch loaf pan.
In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the sugar, butter, and lemon zest on medium-high speed until light, about 3 minutes. Add in the eggs one at a time, until each one is incorporated. Add in the milk and vanilla extract, and beat until well blended, about 1 minute. Add the dry ingredients and beat until just incorporated.
In a small bowl, toss clean blueberries with the 1 teaspoon of all-purpose flour. Gently fold the blueberries into the batter. Scrape the batter into the prepared loaf pan.
Bake until the top is lightly browned and a toothpick inserted comes out clean, about 50 to 55 minutes. (this will depend on the size of your loaf pan). Allow bread to cool in pan for a few minutes then turn onto cooling rack.
While the bread is baking, make the lemon syrup. In a small saucepan, measure lemon juice and sugar, and bring to a boil over medium-high heat, until all the sugar is dissolved and the syrup has thickened slightly, about 2 minutes.
Using a skewer, poke the top of the bread all over. Don’t be shy, you want all the syrup to go into the cake so it will be nice and moist. Brush the bread generously with the lemon syrup. Allow the bread to cool completely, about 2 to 3 hours.
To make the glaze: In a small bowl, mix the confectioners sugar and lemon juice, and whisk to combine. When bread is completely cool, drizzle the top with the glaze.