Prepare a sauté with half of the butter and half of the oil, the spices and the shallots finely chopped. Set the rest of the butter aside at room temperature.
Sprinkle with the vinegar and then add the potatoes. After a few minutes add the cream and a few slices of smoked bottarga. Cover the pan with a lid and bring to simmer, cook until the potatoes are softened. Transfer the content of the pan to a blender and blitz into a smooth soup. Blend in the last half of the butter and season with salt and white pepper.
Plate the velouté and garnish with lime zest, basil oil, caviar, extra virgin olive oil, basil leaves and grated or slice a generous amount of smoked bottarga.