Mix the hoisin and 2 tablespoons soy sauce in a small bowl. Add the cubed tofu, toss, and let marinate for 30 minutes.
Place the cornstarch on a large plate. Remove the tofu from marinade and lay out on cornstarch, tossing to coat all sides. (Reserve the marinade for drizzling at the end.)
Heat the oil over medium-high heat in a large skillet. Add the tofu to the hot oil and fry on all sides. Set aside.
Fill a large saucepan with water and cover. Bring to a boil and add the udon. Cook for 5 minutes and drain. Set aside.
Add the broth, peanut butter, and remaining soy sauce to the same saucepan and bring to a boil. Turn down the heat and cook for 2 minutes, then add the udon back into the pan. Coat the udon with the sauce. Add the spinach to the pot and stir into the sauce and noodles. Continue cooking, on low, for about 3 minutes until the spinach wilts.
Remove from the heat and divide between two bowls. Place half of the tofu on top of each bowl of udon. Drizzle the remaining hoisin mixture over the top.