Prepare the ingredients for the sauce: zest the rind of one lemon and set aside.
Chop walnuts into pieces and roast in a heavy pan over high heat. Stir constantly for about 2 minutes, until walnuts are browned but not burnt.
Set a large pot of salted water to a boil.
In a separate medium-sized pot, combine olive oil, chopped mushrooms and a pinch of salt. Bring to a gentle simmer over medium and then reduce heat to low when oil begins to bubble. Poach for about 10 minutes, monitoring regularly to ensure the oil doesn’t get too hot. (If you see smoke, it’s too hot.)
Remove the pot from the stove and stir in the walnuts. Allow mixture to cool while preparing the gnudi.
In a mixing bowl, combine ricotta, nutmeg, grated cheese and flour. Add salt and pepper to taste. The dough should be sticky but hold together; if not, add a pinch of additional flour.
Bring the pot of boiling water to a simmer. Using a spoon, drop gnudi balls into the simmering water. Work in batches so you don’t overcrowd the pot. The gnudi should hold together; if not, add a little bit of flour to the dough and ensure that the water is simmering.
The gnudi should rise to the surface after about 3 minutes. Transfer in even numbers among 4 individual serving bowls using a slotted spoon. You should have about 3-4 gnudi per bowl.
Before adding the mushroom-walnut sauce, top the gnudi with a sprinkle more of grated cheese, salt and lemon zest. Then cover with the mushroom-walnut sauce including the oil. Sprinkle more grated cheese, lemon zest, and salt on top and finish with torn basil leaves.