1. Heat Oil: In a large pot, heat the vegetable oil over medium heat.
2. Sauté Aromatics: Add the sliced onions, and sauté until translucent. Then, add the minced garlic and grated ginger, cooking for about 1 minute until fragrant.
3. Add Curry Paste: Stir in the red curry paste, cooking for another minute to release the flavors.
4. Pour in Broth: Gradually add the vegetable or chicken broth, stirring well to combine with the aromatics.
5. Add Coconut Milk: Pour in the coconut milk and bring the mixture to a gentle simmer.
6. Season the Soup: Add soy sauce and brown sugar to balance the flavors. Mix well.
7. Add Vegetables: Toss in the mixed vegetables and let them cook for about 5-7 minutes, or until tender.
8. Add Protein: If using cooked protein, add it to the pot, allowing it to heat through.
9. Finish with Lime: Squeeze in the lime juice and stir to incorporate.
10. Garnish and Serve: Serve the soup hot, garnished with fresh basil leaves for an added burst of flavor.

Following these straightforward steps will help you prepare this incredible Thai Red Curry Soup in no time!