No particular web back-end library/framework/toolkit is favoured by the Kotlin community. Perception wise there are slightly more Kotlin developers going for Spring Boot followed by Vert.x. Both back-end systems have very strong Kotlin developer interest and have some Kotlin support (Vert.x provides the best Kotlin support at the moment). Presumably @stokemasterjack is after a back-end system with a reactive style API, official Kotlin support, and a high level concurrency model in which case Vert.x would be an excellent choice.
Vert.x’s API style is a very natural fit (lambdas instead of annotations for explicit APIs which ARE NOT MAGICAL) with the API style commonly found in many Kotlin libraries/frameworks (including the Kotlin standard library). Can already use Vert.x 3.3 with Kotlin via the Java API (works very well), but keep in mind the Kotlin support (the Kotlin API) is in Vert.x 3.4 which is currently under development. A pragmatic strategy to go for is to migrate to Vert.x 3.3 and migrate to Vert.x 3.4 when it is stable (changes between the versions are likely to be small).
Already seen that @stokemasterjack is planning to move from JSP to React which is going to make it much easier to move to the modern Java web frameworks/libraries/toolkits, which in general don’t support Servlets and only use an embedded web server like Netty.