In 2014 I made a wonderful "tea house" trek in the Everest region. I started in Jiri (recommended!), made a loop crossing a few passes and visited Everest Basecamp, Kala Pattar, Gokyo Lakes and some other places. Then walked back to Jiri (looks different when you walk back a month later). Fantastic 319 km walk! (hike report in my signature).
The Jiri - Lukla stretch is lower elevation (1500-3500m, in Nepal they call that "the middle hills"
) but it is much tougher and much more climb/ descend than the Lukla - Everest part. I really liked the Jiri - Lukla (and back) part because it adds a cultural touch to your walk. Unlike Lukla - EBC, it is not a tourist area but you get a real feel of how people live in these remote places.
However, it will probably disappear (or already has?) because when I hiked it in 2014 they had started to build a road...