Trim the cauliflower, removing any green leaves and leaf stems. Remove stem and core; trim and slice into thin pieces. Cut 1 ½ cups of small florets and set aside for later. Coarsely cut the rest of cauliflower into thick slices and chunks.

Melt 2 tablespoons of butter with 2 tablespoons of the olive oil in a large saucepan set over medium low heat. Add shallot, onion, and a pinch of salt and sauté until softened, about 7-10 minutes.

Add water and increase heat to high. Add half the cauliflower chunks and the sweet potato; bring to a boil, then reduce heat to maintain a gentle simmer. Cook for 15 minutes, then add the remaining cauliflower chunks and cook for about 10 to 15 minutes more, or until cauliflower is tender and cooked through and sweet potato is fork tender.

Meanwhile, melt the remaining 4 tablespoons of butter and 2 tablespoons olive oil in a pan. Add the reserved florets and cook over medium heat until browned, stirring occasionally, about 10 minutes. Transfer the florets with a slotted spoon to a small bowl; sprinkle with sea salt. Pour browned butter into a small bowl and set aside.

For popped sorghum, place whole sorghum grains into a brown paper lunch bag. Fold over the top to close. Place in microwave, folded side down. Heat on high for 2 to 4 minutes or until popping sounds are spaced more than 5 seconds apart. Let cool, then pick out popped kernels, discarding duds.

Transfer soup into blender and puree until smooth (use caution when blending hot liquids). Return soup to the saucepan over medium-low heat until heated through. Season to taste with vinegar, salt and pepper, plus additional water if desired for a thinner consistency.

To serve, ladle into serving bowls and drizzle with crème fraîche, garnish with florets, snipped chives, popped sorghum and freshly ground black pepper as desired. Serve warm.