I tried searching the entire internet and came up with 10 different options. none of them worked (forget one click) - wasted 2 hrs per method just to realize it doesn't wrk. I love easy engine and wanted to stick to it - so found an alternate (sleezy) way of doing it..
What I did is fixed my pc hosts file to open the installed website on the ip (ee websites dont open on ip untill this step) : then went there and fetched everything in the existing website via a duplicator / migration plugin (please restrict this to the database only and attachments)
Then just reinstall all the plugins one by one and fetch settings (this way all the crap does not come to the new site - bcz ee is nginx and lamp is well ***** )
This was the best way I could figure out.