Wipe out the pan. Add the closing 1 Tbsp. oil and decrease warmth to medium. Add shallot and cook dinner, stirring in most cases, unless comfy, about 2 minutes. Add garlic; cook dinner, stirring in most cases, unless aromatic, about 1 minute. Add the cauliflower “rice,” thyme, 1/4 tsp. pepper and the closing 1/4 tsp. salt; cook dinner, stirring, for 2 minutes. Add wine; cook dinner, stirring, unless the wine evaporates, 1 to 2 minutes. Add broth; cook dinner, stirring, for 1 minute. Duvet, decrease warmth to medium-low, and cook dinner, stirring about a times, unless the “rice” is extremely comfy, 4 to five minutes. Portray, gain bigger warmth to medium, and add butter. Cook dinner, stirring, unless the butter has melted, about 1 minute longer. Stir in Parmesan, the reserved mushrooms, and the closing 1/4 tsp. pepper.