Unlike Steve (and he's not wrong in suggesting finger joints which are strong), I don't see the need for finger joints here because they are simply doors. Not a whole lot of pressure on the joints... but I wouls avoid 90* cuts on the butt joinery in the middle of the doors. Cut the but joints at any matching angles.
Steve is again correct by suggesting you build 1 oversize door and cutting it in half... but I don't have his equipment so I would build 2 separate doors, both slightly oversized. With any successful "inset" design, doors and drawers faces are always built slightly oversized and trimmed down to the perfect fit.
The major design challenge I see in your desired build will be wood movement. Wood expands and shrinks with the changing seasons but this movement is only across the wood grain - not along. Translated - you will need to allow more space on the top and bottom of your drawers.
Its' never hot or cold in New Hampshire... its' always seasonal.