Coat the bottom of a large pot with one tablespoon of the oil and place it over medium heat. Give the oil a minute to heat up, then add the garlic and ginger. Sauté the mixture for about a minute, until it becomes very fragrant.
Add the broth, coconut milk, and peanut butter. Whisk the mixture well to dissolve the peanut butter in the broth. Add the bell pepper, raise the heat to high, and bring the liquid to a boil. Lower the heat and let it simmer for about 10 minutes, until the pepper is tender and the broth has thickened slightly.
While the broth simmers, cook the noodles according to the package directions, then drain them into a colander when done.
Coat the bottom of a medium skillet with the remaining tablespoon of oil and place it over medium heat. Once the oil begins to shimmer, add the tofu cubes in an even layer. Cook the tofu for about 10 minutes, turning the pieces once or twice, until they're golden brown and crispy. Transfer the tofu to a plate when done.
When the broth has finished simmering, whisk in the brown sugar, soy sauce, lime juice, and sesame oil. Remove the pot from heat, give it a taste-test, and adjust any seasonings to suit your taste. Stir in the cilantro.
Divide the noodles, tofu, and edamame among bowls, then ladle the broth over everything. Sprinkle with toppings and serve.