Barn conversions such as this insulate on the outside of the framework - either with SIPS or rigid foam insulation panels beneath the roof shingles.

The insulation used in the bank barn renovation as seen in the photo is SIPS (structural insulated panels). The existing finish of the roof and exterior walls are left in place and repaired as required using reclaimed wood in order to retain the patina of the existing finishes on the interior. The SIPS panels are then applied to the exterior (paint the interior face of the panel black so it is not visible through the open space between the existing siding). The standing seams of the original roof are flattened so the new SIPS panel can be laid on top.
A new finish material is then applied to the exterior walls and roof that matches the existing in style and color. The results are a well insulated building with all the existing finishes retained on the interior and all new but matching finishes on the exterior.
Critical to retaining the look of the original thin roof eave (typical of many old barns) is in the detailing of the connection between the wall and roof SIPS panels so you avoid seeing the thickness of the SIPS panels at the eaves. Only the top surface of the panel needs to extend over the wall panel. Not the full panel. Otherwise you can get a very thick 8 to 10 inch thick eave where only rafter tails had been previously. New rafter tails can then be added to the underside of the eave to replicate the original look.
No drywall is needed and all the original interior timbers are retained and fully exposed. Electrical wiring can be run within the SIPS panel space or otherwise concealed behind the existing siding.
I hope this is helpful.
Blackburn Architects PC (www.blackburnarch.com)

Thank you all so much. Hoping to break ground soon !