To press the tofu without a tofu press: set a plate on the counter and cover with 2-3 sheets of paper towels. Set the drained tofu block on the towels and cover with 2-3 sheets more. Top with another plate, then set a heavy flat-bottomed object, such as a cast iron skillet. Let sit for 20 minutes. Remove the tofu from the "press" and slice into small pieces. Toss with cornstarch, 1 tablespoon sesame seeds, salt, and pepper.
Start the broth. Heat sesame oil in a large sauce pot or Dutch oven over medium heat. Saute the shallots until soft, about 4-5 minutes, then stir in 4 garlic cloves and the ginger for another minute. Pour in the broth and add the dried shiitake mushrooms, kombu, 1/3 cup of soy sauce, and 2 tablespoons of pomegranate molasses. Bring to a boil, then lower to a gentle simmer for 20-30 minutes. Monitor the water level throughout and taste for soy sauce and pomegranate molasses.
Heat 1 tablespoon sesame or olive oil in a large skillet. Add the coated tofu into the skillet and cook for 10 minutes, tossing every couple of minutes, until all sides are golden. Move to a paper towel lined plate.
In the same skillet, add another drizzle of oil and toss in the mushrooms along with the butter, garlic, remaining sesame seeds, red pepper flakes, and a pinch of salt and pepper. Cook until crisp and caramelized, about 5 minutes.
Back to the broth. Stir in the coconut milk, then drop in the ramen noodles and cook until softened, about 2-3 minutes for most brands.
Divide noodles and broth into four bowls. Portion out the tofu and mushrooms. As desired, serve with jammy eggs, sliced scallions, additional sesame seeds, fresh cilantro, and chopped vegetables such as carrots.