Preheat the oven to 425 degrees. Toss the root vegetables with 2 tablespoons olive oil, salt, and pepper on a baking sheet. Roast for 25 minutes until the edges start to brown.
While the vegetables roast, season the venison medallions with salt and pepper on both sides. Heat the remaining tablespoon of olive oil in a large skillet over medium-high heat.
Sear the medallions for 2 to 3 minutes per side until browned but still pink inside. Remove them to a plate and tent with foil.
Lower the heat to medium and add the shallots to the same skillet. Cook for 1 minute until softened, then add the crushed juniper berries.
Pour in the red wine and beef broth. Simmer for 5 minutes until the liquid reduces by half, scraping up any browned bits.
Stir in the butter until it melts and the sauce thickens slightly. Return the medallions to the skillet and spoon sauce over them for 1 minute to warm through.
Serve the medallions with the roasted root vegetables on the side and spoon the juniper sauce over the meat. Garnish with thyme sprigs.