Bring a large pot of water to a boil.
Once the water is boiling, add pasta and cook according to the directions for your chosen pasta, until al dente.
While the pasta cooks, melt the butter in a large skillet. Once fully melted, allow the butter to cook over medium about 5 minutes more, until the foam subsides and a rich golden brown color is achieved. Pour the brown butter into a separate bowl for now.
In the same skillet, add 1 tbsp olive oil and saute the mushrooms over medium high heat until tender and lightly browned, 7-9 minutes.
In a separate, dry pan, toast the walnuts over medium heat, until fragrant and just beginning to brown, 4-5 minutes, stirring often. Remove from the heat as soon as they are toasted as they can burn quickly.
When the pasta is cooked, drain the pasta, reserving ½ cup of pasta water. Add the pasta to the skillet with the mushrooms, and return to low heat. Stir the pasta, brown butter, walnuts, and pecorino romano into the mushrooms. You can add a splash or two of the reserved pasta water if it looks a little dry.
Serve, topping with extra pecorino romano, salt, and black pepper to taste.