Set a 6 quart Dutch oven over medium-low heat. Add butter and cook gently for 4-5 minutes, stirring frequently, until all liquid has cooked off, milk solids have browned, and it begins to smell nutty. Remove from heat, add shallots, season generously with salt and pepper, and stir to combine, gently scraping browned butter solids from the bottom of the pan. When the vigorous bubbling has subsided, return pan to low flame, and continue to cook shallots until they are translucent and tender, about 5 minutes. Add cauliflower and cook, stirring occasionally, until tender, 3-5 minutes. Add red wine vinegar and continue to cook, stirring occasionally, until all the liquid has cooked off, about 30 seconds to 1 minute. Add milk and vegetable stock, increase flame to medium, and bring to a simmer. Cook, stirring occasionally, until the liquid has reduced by about ¼. Transfer soup to a blender and puree until smooth. Pass through a fine mesh sieve if desired, then season with salt, pepper, and a splash of vinegar to your liking. Serve immediately or chill and store in the refrigerator, covered, up to one week.
