Heat a Dutch oven over medium high heat. Generously season the bison with salt and pepper. Once the pan is hot, add olive oil and sear the bison on all sides. It should form a deep brown crust. Remove the bison from the pan and set aside.
Let the pan cool off. Wipe clean with a paper towel, and reheat over medium. Add second tbsp. olive oil, plus all the veggies. Let them cook for 10-12 minutes, stirring often, until they start to soften slightly. Add root beer, red wine, chicken stock, and tomatoes. Add your herbs. Return the bison shortribs to the pot. Bring to a boil on the stove top, then cover, and place in the oven for 3.5 hours.
Remove meat to a platter, and strain the braising liquid. Pour some of the liquid over the bison. Serve with polenta, or celery root puree, or mashed potatoes. So delicious, the meat should be falling off the bone at this point. Enjoy!