Preheat your oven to 350°F. Coat an 8½ x 4½-inch loaf pan with baking spray to prevent sticking.
In a medium bowl, whisk together ¾ cup all-purpose flour, ¾ cup whole-wheat flour, baking soda, baking powder, cinnamon, salt, and ginger until well combined.
In a larger mixing bowl, whisk together eggs, mashed banana, brown sugar, melted butter, sour cream, vanilla extract, and lemon zest until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring just until almost combined. Be careful not to overmix!
Toss the blueberries with the remaining 1 teaspoon of all-purpose flour, then gently fold them into the batter.
Pour the batter into the prepared loaf pan, spreading it evenly.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean. If the top browns too quickly, cover it loosely with foil during the last 10-15 minutes of baking.
Allow the bread to cool in the pan for 10 minutes, then carefully transfer to a wire rack to cool completely (2-3 hours).
In a small bowl, stir together confectioners’ sugar, lemon juice, and sour cream until smooth. Drizzle over the cooled bread before slicing and serving.