Fill a large pot with water and bring to a boil over high heat. Add a small handful of salt to the water and add spaghetti. Cook spaghetti until al dente, 6 to 7 minutes, stirring occasionally. Drain pasta and set aside.
Place a skillet over medium heat and heat oil. Once skillet is hot add mushrooms and sauté until brown, 2 to 3 minutes. Lightly season with salt and pepper and continue to sauté for an additional 1 to 2 minutes. Transfer mushrooms to a plate and set aside.
Place skillet back onto the stove and add 1 tablespoon butter.
Saute shallots and garlic for 2 minutes. Deglaze with mirin and cook until skillet is almost dry.
Add dashi and soy sauce to the skillet and boil until mixture has been reduced by ½.
Stir remaining butter into the skillet. Add mushroom mixture and pasta to the skillet and toss together until fully and well coated. Adjust seasonings if needed and finish wit a sprinkle of furikake and grated Parmesan. Serve.