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Grate cauliflower with hand grater. Set aside.
Heat oil in large skillet on medium-high heat. Add mushrooms; cook and stir 2 minutes. Add garlic; cook and stir 2 minutes longer or until mushroom are lightly browned, taking care not to burn garlic. Remove from skillet; keep warm.
Bring chicken stock and thyme to simmer in small saucepan on low heat. Set aside on low heat. Add cauliflower to skillet on medium heat. Stirring constantly, add warmed stock mixture, 1/4 cup at a time, until liquid is absorbed by cauliflower after each addition. (It takes about 30 minutes for all of the stock mixture to be absorbed and the cauliflower to become tender)
Stir in mushrooms, cream, butter, Parmesan cheese, truffle oil, sea salt and pepper. Let risotto stand on very low heat 5 minutes to allow flavors to blend. Sprinkle with parsley. Serve with additional Parmesan cheese, if desired.