Add the chicken stock to a small saucepan, cover, set over medium-low heat and bring to a simmer. Meanwhile, add the butter and 1 tbsp of olive oil to a large saucepan and set over medium heat. Once the butter is melted, add the mushrooms and a generous pinch of salt. Cook, stirring, every so often, untilt the mushrooms are deeply golden brown - about 10 minutes.
Add the shallots and garlic to the pan. Cook until soft and translucent - only about 2 minutes. Add the buckwheat to the pan and, stirring constantly, toast the granules for another 2 minutes.
Pour over the wine and stir constantly until it is mostly absorbed and the strong alcoholic smell has cooked off - a minute or two.
Add a ladle-full (about 120ml or ½ cup) of the hot chicken stock to the buckwheat. Stir constantly until the buckwheat has mostly absorbed the stock and if a spoon is dragged along the bottom of the pan, the pan is exposed. Repeat with another ladle-full and continue stirring.
Continue with the additions of chicken stock until the buckwheat is tender and cooked through - about 20 minutes. Stir in the parmesan cheese. Taste to adjust for seasoning, adding salt and black pepper where needed. Serve immediately.