Pre-heat oven to 350 degrees. In a bowl, toss the cauliflower and squash with the ground ginger, a tablespoon of the olive oil, and sesame oil. Place in a baking dish and roast until tender, 25-30 minutes.
In a stock pot over medium heat, warm the remaining olive oil and butter until melted, add the leeks and cook until translucent, about 5-7 minutes.
Add the grated ginger and stir. Mix in the squash, cauliflower, stock, a pinch of salt, and mirin. Stir. Allow to simmer for 25-30 minutes.
With an immersion blender or regular blender, blend until smooth. Add the cream and blend until mingled. Garnish with cilantro or croutons.