Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch cake pan.
Stir milk and vinegar together in a small bowl; set aside to sour for 5 minutes.
Beat white sugar and 3/4 cup butter together in a bowl using an electric mixer until creamy and smooth; beat in eggs, soured milk, baking soda, cardamom, cloves, and nutmeg. Gradually stir in flour until just incorporated. Fold in 1 cup blackberries. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, 25 to 35 minutes. Allow cake to cool.
Beat confectioners' sugar and 1/2 cup butter together in a bowl using an electric mixer until smooth and creamy; mix in 1/2 cup blackberries and milk until frosting is desired thickness. Spread icing on the cooled cake; sprinkle with coconut and pecans.