For the carrot-sour milk mix, first peel and coarsely chop the carrot. Peel the apple as well, remove the core and chop coarsely. Pour into a tall container together with the buttermilk, whole milk, ground sunflower seeds, lemon juice, salt and sugar.
Blend with a hand blender (alternatively use a stand mixer) until smooth, refrigerate if necessary. Pour the carrot-sour milk mix into glasses and serve.