Preheat your oven to 325°F/170°C. Grease and line a 8.5x4.5" loaf pan.
Cut your blackberries. If they're small blackberries, cut into quarters, and if they're large cut into eighths. Toss with 1-2 tablespoons of flour in a small bowl and set aside.
Melt your butter in a microwave or in a small saucepan. Once melted, set aside.
In a medium bowl whisk together the flour, baking powder and salt. Set aside.
In a food processor or large blender, blend together your sugar and lemon zest. Do this for about 20-30 seconds, or until the lemon zest releases their oils and your sugar takes on more of a yellow color.
Stop the food processor and pour in your wet ingredients - melted butter, vanilla extract, fresh lemon juice, 3 eggs and sour cream. Blend together for 20 seconds.
Pour the wet ingredients into the dry ingredients and fold everything together with a rubber spatula. Fold until there are no more streaks of flour. Add in your chopped blackberries and fold those into the batter.
Pour the batter into your prepared pan and tape it on your counter a few times to remove any air bubbles. Bake for 80-90 minutes, a tester should come out clean. After 10 minutes, take it out of the pan and let it cool completely. If your loaf is turning too brown in the oven, cover it with aluminium foil.
Blend your 4 blackberries until you have a thick mixture. Add to the powdered sugar, heavy cream and lemon juice and whisk. Add more powdered sugar if it isn't thick enough, or more cream if it is too thick. Pour over your cooled loaf.
Notes
Butter: I use European style butter, like Kerry Gold, in my recipes. This will make your finished bake much creamier and richer.Salt: If you don't have kosher salt, halve the amount of salt called for in the recipe. 1 teaspoon kosher salt = ½ teaspoon fine salt.Storage: the loaf cake lasts up to 4 days at room temperature, keep it well wrapped. Freezing: slice up your loaf and wrap in plastic wrap. Freeze for up to 2 months. To defrost, take it out of the freezer the night before and let it thaw in the fridge overnight. This recipe method is based from Alice Medrich's food processor pound cake.