Because we wanted to keep the bottom of the roof visible, we had to put another roof on top of the 2x6 fir to hold the insulation and keep out the rain.  The first step was to provide a moisture barrier which we accomplished with tar paper.  The cabin weathered the winter with just this cover to protect it.  The next summer was a wet one and we couldn't start working on the roof until July.

Over the tarpaper we put rows of 2x2s from ridge to eve on 2 foot centers screwed down to the TnG roofing.  Use lots of screws because this is the anchor for your entire real roof and the actual snow load.

We added 2x10 rafters all screwed and toe nailed to the 2x2s so that we could transfer the loads down to the 2x6 fir which is our structural roof.

We added 2x8 blocks between the rafters to stabilize the roof.  The roof was designed to ventilate from eve to peak over the top of the insulation and over the blocks

R-30 batt insulation is installed inside the box structure and a second roof of plywood covers over the top. We had to use 3/4 inch plywood here because of the snow load in our area.  We could have used closed cell foam insulation and reduced the thickness of our roof but this method proved to be quite a bit cheaper.

Finally a second layer of tar paper is laid under the actual roofing, in this case snap-lock metal roofing.  This is an expensive and redundant way to make a roof and the only reason I used it was to leave the log rafters and car decking exposed inside.  It does have the advantage that the entire roof is worked from the top so no scaffold work is necessary.

When people talk about building a log house, they usually get all bound up in the price of the logs.  In actual fact the logs are the cheapest part of the house.  We were able to reduce the price of our roof by using log rafters and reducing the pitch of the roof which reduces its size and cost.  But even so, our roof cost us almost 50% more than the logs.