There are two options.
One, install insulation on the bottom of the roof sheathing and install a new finished ceiling on the bottom of the beams.
- Spray foam is an option to consider to spray directly to the bottom of the roof decking -- this will basically create an unvented roof.
- Any other type of insulation -- fiberglass batts, blown-in cellulose, etc. -- will require you to create a vent channel to vent the roof assembly.
The other option is to remove the shingles and install rigid foam on the top side of the roof and then reinstall the shingles.
For more information:
Check our best attic insulation Q&A to see what other homeowners and contractors are saying about foam insulation, attic venting, etc.