Start by adding the butter to a large skillet over low-medium heat, and melt the butter. Then add the onions, and saute until they are translucent, in the last, 30 seconds add the diced carrots and celery, and contine to saute, until they are softened about 4 to 6 minutes.
Slowly add in the cauliflower.
Mixing well, continue to simmer for another 12 to 15 minutes, or until the vegetables are softened.
Slowly pour in the chicken broth, and parsley, and mix well.
The sauce is made by whisking together milk, flour, and butter in a saucepan over low heat. Once the mixture has thickened, it is seasoned with salt and pepper to taste.