PHP framework that provides equivalent to asp.net .ASMX?

PHP framework that provides equivalent to asp.net .ASMX?

I have searched and everything I get looks to be about a PHP app consuming
an .aspx web service but that's not what I'm looking for.
I may be overlooking something obvious and would be happy to hear that but
that doesn't mean I haven't tried.
I'm a .Net developer by platform, a developer by trade 20+ years and will
admit that I'm spoiled by the ease of .Net
That said, an ASP.Net .asmx web service is quite literally a single file
that might be pure soap (but it's so well hidden that I don't know) but I
can use them with jQuery AJAX calls effortlessly. Methods exist that have
parameters (basic types or complex objects defined by classes in my
project) and I can call those methods at a single url, pass in my JSON and
.Net gives me an object to work with. I do what I need, then return an
object matching the methods return type and all the
HTTP/JSON/ENCODING/DECODING is done for me so I only need to worry about
the JSON client-side, working with my classes server side, and treating
the methods like any other server-side method.
Does a library/framework exist for PHP that provides that same sort of
ease? From my reading, I think that 'routing' is a related concept but
that term isn't one I know in the .Net context so assume I know nothing
but basic PHP skills (nothing but server side syntax, operators, data
types, etc..)
I want to learn to love PHP but this could be make/break for me because
everything I do now ends up being client-side JS/DOM and server-side data
management. Very little use for actually manipulating the HTML returned to
the client (Call it Google-style web apps).
If it helps define what I'm looking for, I use Telerik Kendo DataSource a
lot and need the easiest way to focus on my client-side code with Kendo
and actual business logic/db server-side.
Slimframework.com looks to be the closest thing I've found so far but it's
not clear to me if it's intended for what I'm needing or if it's perhaps
just a common tool that would help get me there. I'm hoping for something
clearly more complete.