Recover parameters for stored procedure from system logs
There is no built-in logging mechanism that runs by default out-of-the-box to capture stored procedure parameter values.

Depending on the version of SQL Server you're using, the best way to capture that detail is via Extended Events (actual execution plans and looking at parameter runtime values. Pretty expensive though, and a bear to parse out via XML).

I suppose "best" is very subjective.  I don't think there is really a great, low-impact, way to get the actual parameter values for every execution of a stored proc through some SQL Server built-in mechanism.  It's probably easier to log that through the client, or via logging built into the stored proc.