In a large skillet, melt the butter over medium heat. Add the shallot and cook until softened and fragrant, about 3 minutes. Add the garlic and sauté a minute longer. Add the mushrooms, salt and pepper, and cook until the mushrooms are softened, about 5 minutes.
Add the wine to deglaze the pan. Once the liquid is reduced, add the goat cheese and cook until it’s incorporated into the mushrooms.
Add the mushroom mixture to a food processor along with the walnuts and process until combined but still retaining a bit of a crunchy texture. (This can also be made up to 2 days in advance. The flavor gets better with time.)