Heat oil in a heavy based skillet or pot over medium high heat.
Add curry paste (and garlic, ginger and lemongrass Extras, if using) and cook for 2 to 3 minutes until it mostly "dries out" - see video. Don't breath in the fumes!!
Add chicken broth and coconut milk, mix to dissolve paste.
Curry in a jar seasonings: Add 1 tsp fish sauce, 1 tsp sugar, no salt.
Homemade curry paste seasonings: Add 3 tsp fish sauce, 3 tsp sugar, ⅛ tsp salt.
Add kaffir lime leaves. Mix then bring to simmer.
Add chicken, stir then lower heat to medium so it's bubbling gently. Cook 7 minutes.
Add eggplants, cook 5 minutes until soft.
Taste sauce. Add fish sauce or salt for more saltiness, sugar for sweetness.
Add snow peas, cook 2 minutes until a bit softened, then stir through basil and lime juice. Sauce should have reduced but will still be a be on the thin side, not thick - that's how it's should be. DO NOT keep simmering - sauce will darken.
Serve curry over jasmine rice with garnishes of choice.