Place yogurt and 1/4 cup milk in the work bowl of a food processor or blender and blend until combined. Remove and set aside.
Place frozen blueberries in the work bowl of a food processor or blender. Add remaining milk and puree until smooth. Remove mixture and set aside.
Pour both the yogurt and the blueberry mixture into glasses at the same time. Swirl the different mixtures with a spoon and serve.
Makes 4-6 servings.