Heat the oven to 400℉ and prepare the vegetables. Cut both ends off the butternut squash before slicing it vertically in half and scooping out the seeds. Slice the yam in half, chop the onion into large chunks, and peel the garlic cloves.
Place the prepared squash, yam, onion, and garlic on a metal baking sheet. Then drizzle with olive oil and sprinkle over the brown sugar and allspice. Season with salt and pepper.
Roast for about 30 to 40 minutes, or until the squash and yam are almost fork tender.
Allow the roasted vegetables to cool for about 10 minutes, or until cool enough to handle. Then scoop out the flesh of the squash and the yam, discarding the skins, and transfer to a pot or Dutch oven along with the onion and garlic.
Add the vegetable broth, and stir to combine. Then bring the mixture to a simmer over medium heat. Reduce the heat to low, cover with a lid, and simmer gently for about 20 minutes.
Remove from heat. Using an immersion blender (or stand blender that is safe for hot liquids), blend everything together until velvety and smooth.
Place the soup back over low heat and stir in the heavy whipping cream, as well as the cayenne if desired. Taste for seasoning, and adjust as needed. Continue heating over low just until the soup has reached the serving temperature you prefer.