Creamy Orzo Risotto with Meyer Lemon and Wild Mushrooms

Name: Creamy Orzo Risotto with Meyer Lemon and Wild Mushrooms
Ingredients: 6 cups chicken stock; 6 tbsp. unsalted butter; 8 oz. hen of the woods, chanterelle, or morel mushrooms, cleaned and halved if large; 3 medium shallots, minced; 2 cloves garlic, minced; 1 3⁄4 cups (12 oz.) orzo; 1 tsp. freshly grated Meyer lemon zest, plus 1 tbsp. juice; 1 tsp. minced fresh thyme; Kosher salt and freshly ground black pepper, to taste; 1⁄2 cup cream; 1⁄2 cup finely grated parmesan, plus more for serving