I read through the code and did some other reading too. But while exploring on stackoverflow and such, I came upon this [0] question.
I am now assuming that since author here did not mention a separate thread-pool, the worker thread pool was used up for the the sleep statement as well and thus his concern?
More interesting however is the reply where the person who replied claims undertow is not meant for such cases and mentions his fork undertow-async [1].

Any thoughts around that?

[0] https://stackoverflow.com/questions/47464828/undertown-async-responce-with-another-thread
[1] https://github.com/hank-whu/undertow-async

On Tue, Feb 26, 2019 at 5:50 PM Bill O'Neil <bill@dartalley.com> wrote:
Take a look at the various dispatch methods on HttpServerExchange. They allow you to dispatch from the IO thread to the worker pool or to a custom executor. BlockingHandler is a convenience handler for dispatching to the worker thread pool.

On Tue, Feb 26, 2019 at 5:13 AM Girish Sharma <scrapmachines@gmail.com> wrote:
Hi,

I have been trying to find some solid examples for using Observables/Callbacks/Futures to delegate long running tasks (which return the response to be sent back) over to separate threads. The idea is that the handler method simply spawns an async task and whenever that async tasks completes, we send back the response without making the handler method/worker threads wait for the async task to finish.

Any pointers/examples would be appreciated.
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Girish Sharma
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Girish Sharma
B.Tech(H), 
Civil Engineering,
Indian Institute of Technology, Kharagpur