Not sure if "basement roof" is the right term for this...
My houses concrete foundation has a small extension, which sticks roughly 2-3 feet out from the rest of the foundation for a space of about 4-5 feet. This results in roughly 10 sq ft of additional basement space beyond what the floors above have. There is a small "roof" on top of this space; it is framed with wood and covered in shingles.
Currently these is no insulation in this space at all, and this "roof" is a source of heat loss (anecdotally, and based on thermal imaging). It seems the right thing to do would be to insulate here to mitigate this... but how? It's a sloped wooden structure covered in shingles that keeps rain and snow out of the interior, but it is not at the top of the house and doesn't have a soffit/vent. Is it really a roof?
Does there need to be a moisture/vapor barrier (and which way should it face)? Would foam board or rockwool/fiberglass be more appropriate? Do I need any kind of baffle to allow air flow? (The top of this "roof" meets the bottom of the siding on the house)
I'm in Massachusetts; winters are typically between 0-30F (occasionally a bit colder, especially with wind chill) and summers are typically 70-90F (occasionally but rarely a bit over 100).
The "roof" bit is about 5-6 feet above the ground directly below it and along most of this side of the house, but is about level with the ground just a couple feet away at the corner and around most of the rest of the house.