Mix olive oil, white sugar (if using), distilled white vinegar, fresh basil, black pepper, and kosher salt in a small bowl. All ingredients must be well mixed.
Afterwards stir in the Dijon mustard and full-fat sour cream. Whisk until you have a creamy and velvety dressing.
Gently fold in the blue cheese, taking care to break it up with a spoon or spatula as you do so. The dressing should have an indulgent and luxurious texture now.
If needed, add a few tablespoons of water to thin the mixture out.
To finish, stir in ¼ teaspoon of balsamic vinegar until all the ingredients are incorporated.
Sample and season to preference, then drizzle over your favorite salads before serving.