Prepare the rice noodles according to package instructions. Drain and set aside.
In a large pot or Dutch oven, heat the vegetable oil over medium heat.
Add the minced garlic and ginger, sauté for 1 minute until fragrant.
Stir in the Thai red curry paste and cook for 2 minutes, stirring constantly to release the aromas.
Pour in the coconut milk and vegetable broth, stirring to combine with the curry paste.
Add the soy sauce and brown sugar, stir well.
Bring the soup to a gentle simmer over medium heat.
Add the red bell pepper, snap peas, shiitake mushrooms, and carrot to the pot. Simmer for 5 minutes until the vegetables are tender but still crisp.
Gently add the tofu cubes to the soup and simmer for another 3 minutes to heat through.
Add the lime juice, chopped cilantro, and Thai basil leaves. Stir gently to combine.
Season the soup with salt and freshly ground black pepper to taste.
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 sliced scallions and optional red chili slices.
Serve immediately and enjoy your Thai Red Curry Noodle Soup with Tofu.