Preheat oven to 350 degrees. Spray a 9x5-inch loaf pan with baking spray with flour.Line the bottom of the pan with parchment paper.
In a large bowl, whisk together 2 1/4 cups flour, sugar, and salt.In a medium bowl whisk together the buttermilk, egg, melted butter, vanilla extract, and lemon zest.
Make a well in the middle of the dry ingredients and add the wet ingredients.Use a wooden spoon or rubber spatula to mix together. Set aside 1/2 cup of the batter.Spread half the remaining batter into the bottom of the loaf pan.
In a bowl, toss the blackberries with 1 tablespoon of flour. Scatter half the blackberries over the batter in the bottom of the loaf pan.
Spread the remaining half of the batter over the blackberries.Scatter the reamining blackerries over the batter.
Spoon the set aside 1/2 cup of batter on top.
Bake for 50 to 55 minutes. Let cool in pan for 10 minutes and then remove.
To make glaze, whisk together all ingredients in a bowl. Drizzle over cake.
If the cake starts to get too browned before it is done, place a piece of foil over it.