Place the wild mushrooms in an oven-safe dish and toss with the olive oil. Season to taste with garlic powder, ground ginger, chili powder, salt, and pepper.
Roast the mushrooms for about 30 minutes, until softened and browned. Remove from the oven and roughly chop.
Heat the butter in a large pot over medium heat and sauté the onion and garlic until softened.
Add the riced cauliflower and continue cooking for 2-3 minutes.
Stir in the chicken stock, bring to a boil, and simmer, covered, for about 10 minutes, stirring occasionally.
Season to taste with dried basil, dried parsley, salt, and pepper. Stir in the cheeses and continue simmering for 5-10 minutes.