Combine the vinegar, Parmesan, shallot, garlic, oregano and red pepper flakes in a microwave safe bowl. Microwave on high for 30 seconds or until the cheese is melted and the mixture is fragrant. Set aside to cool.
In a tall sided 2-3 cup measuring cup or bowl, combine the mayonnaise, sour cream, basil and vinegar mixture. Using an immersion or stick blender, process until smooth. With the blender on, slowly add the olive oil and blend until incorporated, about 1 minutes. Season with salt and pepper (more or less to taste) and serve immediately or refrigerate until needed. The dressing will thicken when refrigerated. If overly thick, allow the dressing to come to room temperature for about 30 minutes before serving.
Notes
Refrigerate leftovers in an airtight container. Dressing will keep up to 4 days.
This is a hearty dressing and is best served on crisp lettuce such as iceberg or romaine.