Slice mushrooms and asparagus into ¼ inch pieces, leaving the asparagus tips in 1 ½ inch pieces. Combine broth and water in a saucepan and bring to a boil. Add asparagus and cook until tender (3-4 minutes). Remove asparagus with a slotted spoon and place in ice water. Continue to simmer the liquid.
Heat oil and 1 tablespoon of butter in another saucepan over medium-high heat. Add mushrooms and sauté until brown (about 4 minutes). Place in a bowl, season with salt and pepper and set aside. Using the same saucepan, add 2 tablespoons of butter and melt over medium heat. Add onion and sauté for 3 minutes. Add rice and cook for 1 minute, stirring constantly. Add wine and continue stirring until liquid is absorbed. Add 1 cup of the simmering brother to the rice until absorbed, stirring constantly. Repeat, adding ½ cup of broth until the rice is tender and creamy (about 20 minutes).
Remove from heat, stir in cheese and 1 tablespoon of butter. Stir in asparagus, Shiitake mushrooms and season with salt and pepper to taste. Let stand for 1 minute and serve.