Heat the vegetable oil in a large pot over medium heat.
Add the chopped onion and cook until translucent, about 5 minutes.
Add the minced garlic and ginger, and cook for another 2 minutes.
Add the sliced red and yellow bell peppers, carrots, zucchini, broccoli florets, and snap peas. Cook for about 5 minutes, stirring occasionally.
Pour in the vegetable broth and bring to a boil. Reduce heat and simmer for 10 minutes.
Stir in the coconut milk, red curry paste, soy sauce, and lime juice. Simmer for another 5 minutes.
Season with salt and pepper to taste. Garnish with fresh cilantro before serving.