In a medium saucepan, combine fresh blackberries, granulated sugar, and lemon juice. Cook over medium heat for about 10 minutes, stirring gently until the mixture thickens and bubbles form. Strain the mixture through a fine sieve to remove seeds, leaving you with blackberry purée.

Preheat your oven to 350°F (177°C). Grease and flour a standard loaf pan or coat it with non-stick spray.

In a large bowl, sift together the cake flour and salt. Set this mixture aside.

In a mixing bowl, beat softened butter and granulated sugar together until light and fluffy. Gradually add in vanilla extract and eggs, mixing well.

With the mixer on low speed, gradually add in the dry flour mixture, alternating with sour cream. Beat just until combined.

Set aside half a cup of plain batter and gently fold the blackberry purée into it.

Pour half of the plain batter into the loaf pan, layer with blackberry batter, followed by the remaining plain batter. Swirl gently with a butter knife.

Bake in the preheated oven for 60-70 minutes until a toothpick inserted in the center comes out with moist crumbs.

Remove the cake from the oven and let it cool in the pan for 20 minutes before transferring to a wire rack.

While cooling, prepare the icing by mixing blackberry juice with powdered sugar, milk, and vanilla until smooth.

Once the cake is completely cooled, pour the blackberry icing over the top and serve.