6 cups chicken or vegetable stock
5 tbsp. unsalted butter
8 oz. hen of the woods, chanterelle, or morel mushrooms, cleaned and halved if large
1/2 cup minced shallots
1 tablespoon minced garlic
1¾ cups (12 oz.) orzo
1 tsp. minced fresh thyme
salt and freshly ground black pepper, to taste
½ cup cream
½ cup finely grated Parmesan, plus more for serving
Heat chicken stock in a small saucepan over medium heat; set aside and keep warm. Heat butter in a 4-qt. saucepan over medium-high heat. Working in batches, add mushrooms and cook until golden, 5–7 minutes. Using a slotted spoon, transfer mushrooms to a bowl; set aside. Add shallots and garlic to saucepan; cook, stirring, until soft, 3 minutes.
Add orzo, thyme, salt, and pepper; cook 2 minutes. Add reserved stock ¼ cup at a time, cooking until each addition is absorbed before adding next amount. Cook, stirring often, until liquid has all been used and orzo is tender, about 25-30 minutes. Add cream and cook, stirring, until liquid is creamy, about 3 minutes more. Remove from heat and stir in reserved mushrooms, Parmesan, salt, and pepper; serve with additional Parmesan on the side.