Heat chicken stock in a small saucepan over medium heat; set aside and keep warm.
Heat butter in a 4-quart 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, zest, thyme, salt, and pepper; cook 2 minutes.
Add reserved stock 1⁄4 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 30 minutes.
Add cream and cook, stirring, until liquid is creamy, about 3 minutes more.
Remove from heat and stir in reserved mushrooms, lemon juice, parmesan, salt, and pepper; serve with additional parmesan on the side.