how can I break such a connection so I can reconnect later on
Just kill the pppd process as root :
if the process is not killed softly run :
killall -9 /usr/sbin/pppd
which is more radical.
And to reconnect later re-run as root:
/usr/sbin/pppd call eagle-atm &
The '&' character put the process in background running task.
If you don't want to be root to do that, use sudo and give a user the permission to run these commands.
see 'man sudo'.
Have a good day.