Arrange the yams in a medium saucepan and cover with 2 inches of cold water. Bring the yams to a boil over medium-high heat, and then reduce the heat to medium-low and cook the yams, uncovered, for 30 minutes or until tender. (If you use red-skinned potatoes, the cooking time may be shorter)

Meanwhile, preheat the oven to 350 degrees F. Grease a 9x13-inch casserole dish with the coconut oil.

When the yams are done, drain them in a colander, allow them to cool enough to be handled, and then peel off their skins (the skins should come off easily). Transfer the peeled yams to a large bowl and then mash them with a potato masher or a fork.

Next, stir in the coconut yogurt, egg replacer and water mixture, and the coconut milk. Add the broccoli, salt and pepper and stir, mixing well so that all the ingredients are incorporated. Adjust the seasoning to taste.

Spoon the yam mixture into the prepared casserole dish. Cover the casserole dish with aluminum foil, being careful not to touch the casserole, and bake for 45 minutes. Uncover and bake for another 15 minutes. Allow the terrine to set for about 15 minutes before slicing into squares. Serve hot.