Heat the vegetable oil in a large skillet or wok over medium heat. Add the onion, bell pepper, garlic, and ginger. Cook for 2-3 minutes until the vegetables are softened.
Add the Thai red curry paste to the skillet and stir well to combine with the vegetables.
Pour in the coconut milk and stir until the curry paste is fully dissolved into the coconut milk.
Add the cubed eggplant to the skillet and stir to coat with the curry sauce. Allow the mixture to simmer for about 10-15 minutes, or until the eggplant is tender.
Stir in the soy sauce, brown sugar, and lime juice. Season with salt and pepper to taste.
Once the eggplant is cooked through and the sauce has thickened slightly, remove the skillet from the heat.
Serve the Eggplant Thai Curry hot over cooked rice, garnished with fresh cilantro.