Whisk mayonnaise, vinegar, lemon juice, and Dijon in a medium bowl until smooth.
Slowly stream in olive oil while whisking to create a creamy emulsion.
Stir in Parmesan, sugar, garlic powder, onion powder, Italian seasoning, parsley, salt, black pepper, and red pepper flakes.
Whisk in water a little at a time until the dressing is pourable.
Taste and adjust seasoning. Cover and chill 30 minutes for flavors to meld before serving.