You can either boil the unpeeled sweet potatoes until soft, or you can roast them in a hot oven whole. Once soft, leave them to cool, and peel.
Place the sweet potatoes, and the rest of the ingredients in a food processor, and blend until very smooth. If too thick, add a bit water or milk (1 tbs at a time).
Place all ingredients, except the charcoal into the food processor, and blend until smooth. Adjust the thickness by adding water, or more mayonnaise.
Carefully twist the charcoal capsules, and dump the powder into the food processor. Blend a few more minutes, until the charcoal powder has been fully incorporated. Add more or less to control the desired black color.
I buy my activated charcoal capsules online.