Warm a wide large heavy-bottomed pan over a medium-low flame. Add 2 tablespoons olive oil and 2 tablespoons butter and melt together. Add shallots and cook for 2 minutes, or until translucent, and then toss the mushrooms, thyme, and bay leaf into the pan. Cook for 10 minutes, stirring occasionally, until the mushrooms have released their moisture and begin to turn golden brown.
Pour 1 cup of the wine into the pan, and bring the liquid to a simmer, allowing the wine to evaporate. Continue cooking until the mushrooms are dry, about 5 to 7 minutes. Season with sea salt and freshly ground black pepper. Remove mushrooms from the pan and set aside. Discard the bay leaf.
Reduce the flame to low, and add the remaining butter and oil to the pan and melt. Stir in the rice and coat with the oil until the kernels are shiny, about 3 to 5 minutes. Pour in the remaining 1 cup of white wine and let evaporate.
Add the chicken broth, 1 ladle at a time, allowing the rice to absorb the liquid. Do not add too quickly so as to prevent the kernels from exploding. Stir over a gentle flame until each ladle of the liquid is absorbed. Repeat until most of the broth is incorporated and the risotto rice is al dente, about 25 minutes.
Fold the mushrooms back into the rice and season with salt, pepper and parsley. Stir in the Parmesan and finish with slices of white truffle, if available. Serve immediately.
Put the chicken, vegetables, and giblets in a large stockpot over medium heat. Pour in enough cold water to cover by 1 inch (about 3 quarts); too much water will make the broth taste weak. Toss in the herbs and peppercorns and allow it to slowly come to a boil. Reduce the heat and gently simmer for 1 hour, uncovered, until the chicken is done. As the stock cooks, skim any impurities that rise to the surface; add a little more water, if necessary, to keep the chicken covered while simmering.
Carefully remove the chicken to a cutting board. When it is cool enough to handle, discard the skin and bones; hand-shred the meat into a storage container and reserve for soups and salads.
Strain the stock into another pot through a fine sieve or a strainer lined with cheesecloth to remove excess fat and the vegetable solids. Use the stock immediately, or if you plan on storing it, place the pot in a sink full of ice water and stir to cool down the stock. Transfer to a storage container, cover and refrigerate for up to 1 week, or freeze for up to 6 months.