Heat a large pot over medium heat. Add olive oil and 1 tablespoon butter, then add onions with a pinch of salt. Stir to coat and cook until softened, about 5 minutes. Add in chopped cauliflower and vegetable stock, then cover and cook for 20-25 minutes until softened. A few times during cooking, use your spoon to press down and break apart or mash the cauliflower.

While cauliflower is cooking, make the chive oil. Combine the chives and olive oil in a blender or food processer and blend until totally smooth. If needed, you can strain the oil thru a very fine mesh strainer. To fry the capers, heat a small skillet over medium-high heat and add 1-2 teaspoons of olive oil. Add dry capers and shake the pan or stir, tossing for 1-2 minutes until crispy and fried. Set aside to drain on a paper towel.

Once the cauliflower is soft, scoop it (and all the remaining broth) into a large bowl. Add half of the mixture to a blender with half cup of water and puree until smooth. Once smooth, add back to the pot and puree the remaining cauliflower mixture with the other half cup of water. Add to the rest.

Heat over low heat, stirring in milk or cream and remaining butter. Taste and season with salt and pepper, then garnish with additional roasted cauliflower (I roasted at 425 with olive oil, salt + pepper for 40 minutes, tossing), capers and chive oil.