Feel free to use the oven for this one, like most do - but for me, I fired up the RecTeq to 350f and got ready for the cook.
In a small saucepan, go ahead and add that red Wine, garlic, and thyme. Bring it to a simmer, watch your liquid level and reduce by half.
Get your dutch oven out and prepare to sear some deer. Throw some ghee in, coat the bottom and get a good sear on the venison. When it's good on colored, remove it while we're cooking the veggies.
With the leftover ghee and deer liquid in the dutch oven, add in that carrot, celery, and onion and cook it down until onion translucent (5min).
Go ahead and add the beef stock and our red wine reduction (obviously the deer as well) to our dutch oven - pop the lid on it - and put it in the oven (or RecTeq) for about 2 hours.
Contrary to the "If you're looking, you ain't cooking" mantra, after the first hour, give it a peek every 20-30 minutes until it's where you want it - for me 2 hours. Shovel it onto a plate and enjoy the fruits of your labor.