Mix the Thai green curry paste with the coconut milk in the slow cooker.
Add all the remaining ingredients apart from the pepper, mangetout and baby corn (these will be added half an hour before the end so that they don't go too soft).
Switch the slow cooker on and set it off on low for 4 to 5 hours or high for 3 to 4 hours.
Half an hour before you are ready to eat, add the vegetables.
If you have added them, remove the lemongrass and kaffir lime leaves and serve with rice or noodles.
Notes
Note 1: My preferred brand of Thai Curry Paste is Mae Ploy. This is available in most supermarkets, if not I sometimes get it on Amazon. The amount of paste you use may depend on the brand, for Mae Ploy I find 3 tbsp is perfect for a slow cooker curry.Note 2: Palm sugar is more typical in a Thai curry which is available in supermarkets, but if you don't have it you can use brown sugar instead. You can also leave the sugar out altogether if you prefer.Note 3: if you can't get hold of any kaffir lime leaves don't worry too much, especially if your curry paste has kaffir in it (Mae Ploy does). If you want you can add a tiny squeeze of fresh lime juice and a small pinch of fresh lime zest right at the very end of cooking. Note 4: fresh green chillies are completely optional because Mae Ploy green curry paste is already highly concentrated and inherently very spicy. The paste gets its signature green color and heat directly from green chillies, so unless you want some extra heat you can leave them out.