Heat vegetable oil in a large pot over medium-high heat. Add onions and salt, cover, reduce heat to medium, and cook, stirring occasionally, until onions are very soft, 5 to 8 minutes. Add garlic and wine. Cook, stirring, until liquid is almost completely evaporated, 3 to 5 minutes.
Stir in cauliflower and broth and bring to a boil. Reduce heat to a simmer, cover, and cook until cauliflower is very soft, 20 to 25 minutes.
In 3 batches, whirl soup in a blender until very smooth, at least 3 minutes per batch (or, if you'd like a few florets in your soup, blend 2 batches and leave the last chunky). Stir together and season to taste with white pepper and salt.
In a small bowl, combine olive oil, chives, and parsley. Ladle soup into bowls and decoratively drizzle herb oil on top.
Note: Nutritional analysis is per 1 1/2-cup serving.