Melt 1/2stick of the butter in a heavy pot over medium heat. Then add the onions and cook until translucent, about 3 minutes. Add the carrots and celery, and then stir and cook for a couple more minutes. Throw in the cauliflower. Then stir it around, cover and cook over very low heat for 15 minutes.
Add the parsley, and then add the chicken broth and simmer for 10 minutes.
Meantime, make a simple white sauce: Melt the remaining 1/2stick butter in a medium saucepan over medium heat. Then whisk in the flour. Cook for a couple of minutes, and then pour in the milk, whisking to combine. Remove the white sauce from the heat and pour in the half-and-half. Then pour this creamy mixture into the pot. Add 1 teaspoon salt and pepper to taste, and allow the soup to simmer for another 20 to 30 minutes. The soup will thicken slightly but shouldn't be overly thick. Give it a taste and add more salt if needed.
Now, this is the fun part: To serve the soup, place the room temperature sour cream in the bottom of a soup tureen (a very large serving bowl). Then add the whole pot of hot soup to the tureen.
Stir gently to combine, and then serve immediately with warm rolls and an appetite for something wonderful.
You will love everything about this.
Variation: For a smoother, thicker soup, use an immersion blender to puree. Simmer an additional 10 minutes after pureeing.