Place cauliflower flowerettes in a food processor and pulse until small pieces of "rice" (or use a cheese grater).
Heat 2 tablespoons oil in a large saucepan over medium-high heat. Add the mushrooms, and cook until soft, about 3 minutes.
Remove mushrooms and their liquid, and set aside.
Add 1 tablespoon oil to skillet, and stir in the shallots. Cook 1 minute.
Add cauliflower rice, stirring to coat with oil, about 2 minutes. Add 1/4 cup broth to the "rice," and stir until the broth is absorbed. Stirring, until the liquid is absorbed, about 5 minutes.
Remove from heat, and stir in mushrooms with their liquid, butter, chives, and parmesan. Season with salt and pepper to taste.