I'm redoing my entire roof (roof deck included). The previous owner built a carport parallel to the house. The carport is a permanent structure with a normal roof - trusses and whatnot of equal quality to the house itself.
The two roofs are parallel. They come together at a valley roughly 12 feet long with almost zero slope in the valley itself. I'm worried that water will run down either roof and just stay in the valley. How can I flash this properly so it will not leak?

Responding to Ecnerwal:
Are you talking about something like this?
