Start by cleaning and preparing your vegetables. Trim the cauliflower and broccoli into florets for easy dipping. Take the other and cut them into large quarter slices. Keep in mind that you and your guests will use skewers or toothpicks to dip into the bagna calda.
Once prepared, heat the butter, oil, garlic, and anchovie filets on medium to low heat. Skim some of the bubbles from the butter and discard. Occasionally stir the to melt away the anchovies. Keep the heat on low, and if possible transfer to a fondue plate or some type of warming dish. When you are ready, dip your vegetables, and bread into the bagna calda, and enjoy with a glass of your favorite wine. After having this as an appetizer, I thought that it would also be good drizzled over steamed vegetables later in the week.