Brush the mushrooms clean with a dry cloth or brush instead of rinsing them. They absorb water like a sponge, and that water will release in the pan, causing them to boil instead of fry, meaning they will never get that concentrated flavor. Cut larger ones into thick slices and leave the small ones whole.
Heat two tablespoons of olive oil in a frying pan until very hot and fry the mushrooms in two batches. Stir only once they are browned on one side and season with salt at the end, as salt draws out moisture. Add a finely chopped clove of garlic and some thyme during the last minute, then set aside.
Rinse the buckwheat until the water runs clear. Sauté the finely chopped shallot in the remaining olive oil until translucent, add the second clove of garlic and the buckwheat, and stir for a minute. Deglaze with the white wine and let it evaporate.
Pour in the stock in batches, letting the buckwheat cook while stirring for about twenty minutes until tender. Buckwheat binds less than risotto rice, so it will remain looser in texture; the creaminess will come from the butter and cheese later.
Stir in the butter, grated Parmesan, and some lemon zest, and season to taste. Spoon the mushrooms on top and finish with coarsely crushed walnuts and parsley.