Heat the vegetable oil in a large pot over medium heat.
Add the garlic and ginger, and sauté for 1-2 minutes until fragrant.
Add the carrots and bell peppers, and cook for another 3-4 minutes.
Pour in the vegetable broth and coconut milk, and bring to a simmer.
Stir in the red curry paste and soy sauce, and let it simmer for 5 minutes.
Add the rice noodles and cook according to the package instructions.
Once the noodles are cooked, stir in the spinach, lime juice, and brown sugar.
Serve the soup hot, topped with bean sprouts, cilantro, and green onions.