Remove all fat and silver skin from the venison. Season with Cajun seasonings and let sit for 30 minutes.
Dredge in flour to coat and shake off excess flour.
Melt 2 tbsp butter and olive oil over medium heat in a large skillet.
When foam subsides, add meat and brown on both sides. Remove the chops and place on a warm plate.
Pour most of the fat off from the skillet. Add the wine and 1/4 cup of the stock. Bring to a boil over high heat for 2 minutes, scraping the bottom and sides of the skillet.
Reduce heat to low and add the venison back to the skillet and cook until medium rare, basting the meat with the sauce. Transfer the meat to a serving platter.
Add remaining 1/2 cup stock and any juices from the meat to skillet and bring back to a boil, scraping bottom and sides of skillet.
When sauce has reduced to a thick, syrupy consistency, remove from heat and season with salt and pepper to taste. Stir in 2 tbsp softened butter. Pour sauce over meat.
Serve with a rice side dish.