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Bring a large pot of salted water to a boil over high heat. Cook pasta based on package directions.
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Meanwhile, heat 1 tablespoon of the oil in a large pot over medium-high heat. Season steak with salt and pepper. Add half of steak and cook, stirring often, for 2 minutes, until browned. Remove from pot and brown the second half of the steak.
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Add the first half of the steak back to the pot with the second half. Add the white and light green parts of the green onions to the pot with the steak and cook for 2 minutes, stirring often. Add the broth, soy sauce, mirin, and brown sugar. Stir to combine. Place the sweet potatoes over the beef. Then add the mushrooms. Add the bok choy on top. (The vegetables don’t all have to be submerged in liquid. The bok choy on top will steam.) Cover and reduce heat to medium. Let simmer until the sweet potato is tender, about 12 minutes.
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While the sukiyaki is cooking, fry the tofu. Heat remaining 2 tablespoons oil in a skillet over medium high heat. Season tofu with salt and pepper. Cook without stirring for 5 minutes, to let the bottom part of the tofu get brown. Flip over the cubes with tongs and cook for another 5-10 minutes. Move the tofu around now and then to let as much as possible brown, especially if you notice one side of your pan is hotter and the tofu there is browning faster than the rest.
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To serve, put cooked spaghetti into bowls. Ladle the beef, vegetable, and sauce mixture over the noodles. Top each bowl with a few pieces of fried tofu and the green parts of the green onions.