Trim stems of mushrooms and slice evenly. Heat skillet and saute mushrooms in olive oil for 5 minutes or until tender and golden. Season with salt and pepper. Reserve 1/3 of mushrooms for the sauce.
Heat stock in a pan and gently simmer. Meanwhile, melt 1 tablespoon of butter in a heavy saucepan on medium heat. Add the onion and saute until soft and translucent, approximately 5 minutes. Add the garlic and cook an additional minute longer. Add the rice and stir with a wooden spoon until rice becomes translucent. Add a ladle of mushroom stock and cook on medium heat until stock is absorbed. Adjust seasoning as needed. Continue to add ladles of stock, repeating the process until rice is tender but still firm.
For making the risotto cakes the consistency should be less creamy than a traditional risotto. Spread the risotto onto a baking sheet to cool.
Season slices of duck liver with salt and pepper. Sear quickly in a heavy saute pan on high heat on both sides until golden brown. Remove and place on towels to absorb fat.
To assemble cakes, place 8 (3 by 1 1/2-inch high) ring molds on a buttered baking sheet. Fill molds with risotto evenly, slightly less than 1/2 full. Place duck liver in center and top off the molds with remaining risotto. Sprinkle a generous amount of Parmesan on top, refrigerate until ready to bake. When ready to bake, preheat oven to 375 degrees F. Remove molds gently and bake in oven for 12 minutes.
For the sauce, melt 1/2 ounce of butter in a saucepan. Saute shallots until slightly browned then add remaining mushrooms and saute for a minute longer. Turn to high heat and add the remaining mushroom stock and reduce by half. Adjust seasoning and finish with remaining butter.
To assemble, toss greens in salt, pepper, olive oil, and balsamic vinegar. Place risotto cakes on plates, spoon sauce around and garnish with tossed green salad. Top with slices of white truffle.