Creamy Orzo Risotto with Meyer Lemon and Wild Mushrooms

Substances:

6 cups chicken stock
6 tbsp. unsalted butter
8 oz. chicken of the woods, chanterelle, or morel mushrooms, cleaned and halved if trim
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 novel thyme
Kosher salt and freshly ground shadowy pepper, to style
1⁄2 cup cream
1⁄2 cup finely grated parmesan, plus extra for serving