Bring a large pot of water to boil.
While the water is being boiled, render the fat from the bacon. In a cold skillet, add the chopped bacon and olive oil. Then turn the heat on to low and cook the bacon for about 8-10 minutes until the fat is rendered and the bacon turns golden. Make sure to stir occasionally so that the bacon doesn't cook too long on one side. Then add the mushrooms in the bacon fat for about 2-3 minutes until they turn golden brown. Turn the heat off and let the pan cool down.
When the bacon and mushrooms are finished cooking, the pot of water should be boiling by then. Generously add salt to the pot of water and cook the bucatini al dente.
While the bucatini is cooking, make the carbonara sauce. In a large bowl, whisk together the eggs, cheese and black pepper. Then whisk together ⅓ cup of the pasta water with the miso. Then vigorously whisk the miso pasta water into the egg mixture to temper the eggs. Then set aside.
When the bucatini is cooked al dente, immediately transfer the pasta to the pan with bacon and mushroom. (Make sure to reserve a cup of pasta water before straining the pasta.) Then add the egg miso mixture to the pan with the hot pasta. Add another ¼ cup of pasta water to the pan and vigorously stir the pasta with the sauce so that it emulsifies and it becomes creamy.
Plate the pasta immediately and top with furikake, grated Parmigiano Reggiano and chopped scallions. Serve immediately because good carbonara waits for no one. Enjoy!