Add the pastes, sauces, and syrup to a large Dutch oven. Mix together until smooth before adding the chicken, mirepoix, broth, and coconut milk. Stir everything together and cover the pot.
If you don't have a Dutch oven, you can use a slow cooker on its high setting with similar cooking times.
Bake at 350ºF on the middle rack for 90 minutes.
Add the gnocchi to the soup after 90 minutes. Cover and bake for another 20-30 minutes until the gnocchi is cooked through and floating.
Transfer the chicken to a separate bowl to shred before adding back to the soup. Stir in a bit of chopped Thai basil before serving.
Garnish with fresh Thai basil, crispy shallots or wonton strips, and a squeeze of lime juice, if desired.
Notes
*Broth note: I made a version with 4 cups of broth instead of 6. If you prefer a thicker soup vs more broth, you may consider reducing the amount or meeting in the middle. You can also add broth when you add the gnocchi if your soup needs more.