Make the sauce: Mix the gochujang, sesame oil, coconut sugar (if using), vinegar, garlic, and 1 tablespoon of water together in a small bowl. Set aside.
Marinate the tofu: In a medium bowl, mix together the garlic, tamari, sesame oil, and coconut sugar. Add the tofu and let the tofu marinate for 10 to 15 minutes.
Prepare the rice: Heat the oil in a cast-iron skillet over medium heat, swirling to coat the bottom of the skillet. Add the rice and pat it into an even later. Reduce the heat to medium-low and let the rice cook, without stirring, for 10 to 15 minutes, until it has a crispy golden crust on the bottom.
Prepare the toppings: While the rice is cooking, heat 1 tablespoon of the oil in a wok or skillet over medium heat, and add the spinach. Sprinkle it lightly with sea salt and cook, stirring frequently, for 3 – 4 minutes, until softened and tender. Transfer the spinach to a bowl and set aside.
Add 1/2 tablespoon of the oil to the same pan, and cook the shiitake mushrooms over medium heat for 2 to 3 minutes, until they have softened and the edges are lightly browned. Add the tamari and cook until any visible liquid has evaporated and the mushrooms are lightly glazed. Set them aside in a small bowl.
Add another 1/2 tablespoon oil to the pan, add the bean sprouts, and sprinkle them lightly with sea salt. Cook for 1 minute, to just heat through and soften slightly. Set aside.
Heat a little more oil in the same pan, and fry the 4 eggs, sunny side up or over easy as desired. Divide the rice among 4 large bowls and set the fried eggs on top of the rice.
Add the tofu to the nonstick pan and cook each each side for a few minutes, until golden. Divide tofu among bowls, placing it next to the egg, and then arrange the spinach, cucumber, mushrooms, seaweed, sprouts, and shredded carrots, in seperate heaps, around the tofu and egg.
Serve with the gochujang sauce on the side, so you can can stir the ingredients together with as much sauce as desired.
Adapted from the bibimbap recipe in the Lucky Rice cookbook by Danielle Chang.