Press the tofu to remove excess moisture by wrapping it in a clean kitchen towel and placing a heavy object on top for 10 minutes.
Heat 1 tablespoon of vegetable oil in a large pot over medium heat. Add the tofu cubes and cook until golden brown on all sides, about 5-7 minutes. Remove tofu from the pot and set aside.
In the same pot, add the remaining 1 tablespoon of vegetable oil. Add the sliced onion and sauté for 3-4 minutes until translucent.
Add the minced garlic and grated ginger to the pot and cook for 1 minute until fragrant.
Stir in the Thai red curry paste and cook for 2 minutes, stirring frequently to release the flavors.
Pour in the vegetable broth and coconut milk, stirring to combine. Bring the mixture to a simmer.
Add the soy sauce and brown sugar to the pot. Stir well and let the soup simmer gently for 5 minutes.
Meanwhile, cook the rice noodles according to package instructions until al dente. Drain and set aside.
Add the sliced red bell pepper, snap peas, and julienned carrot to the soup. Simmer for another 3-4 minutes until the vegetables are tender but still crisp.
Return the browned tofu to the pot and heat through for 2 minutes. Taste the soup and season with salt and freshly ground black pepper as needed.
To serve, divide the cooked rice noodles among four bowls. Ladle the hot red curry soup with tofu and vegetables over the noodles.
Garnish each bowl with chopped cilantro, sliced green onions, and a lime wedge on the side for squeezing.