Heat the coconut oil in a large pot over medium heat. Add the onion and garlic. Cook for 3 minutes until the onion turns soft.
Stir in the Thai red curry paste and cook for 1 minute to release its aroma.
Add the eggplant cubes. Cook for 5 minutes, stirring often so the pieces brown lightly.
Add the red bell pepper and carrots. Stir everything together.
Pour in the coconut milk and vegetable broth. Bring the mixture to a simmer.
Lower the heat and cook uncovered for 15 minutes until the eggplant and carrots are tender.
Remove the pot from heat. Stir in the lime juice and salt. Sprinkle the chopped cilantro over the top before serving.