Heat olive oil in a large saucepan over medium-high heat. Stir in shallot and cook for 30 seconds, then add shiitake and cremini mushrooms, and cook until they begin to brown. Stir in 2 tablespoons butter and Arborio until rice is well coated in oil; reduce heat to medium, and cook until the shallot and mushrooms have turned golden brown.
Pour in white wine, and simmer until evaporated, stirring constantly. Season with thyme, celery salt, salt, and pepper. Reduce heat to medium-low; pour in 1/3 of the hot vegetable stock, and cook until evaporated, stirring constantly, about 7 minutes.
Pour in another third of the vegetable stock, and continue to stir until evaporated. Repeat once more with the remaining third of stock. Stir constantly until the rice is tender and creamy. Add hot water if needed to continue cooking until the rice has softened.
Stir in butter, Parmesan cheese, and chopped parsley before serving.
