Combine the coconut milk, curry paste, and water in the slow-cooker insert. Mix well.
Add the chicken and eggplant. Cover and cook for 4 hours on low or 2 hours on high.
Toss in the green beans and courgettes and combine. Cook on low for another 30 minutes.
Taste and adjust seasoning, if necessary. Serve and sprinkle coriander leaves on top.
Enjoy with a side of quinoa or cauliflower rice.