In a bowl, combine the ground venison, crushed croutons, Dijon mustard, egg, parsley, and salt. Using your hands, gently mix until just combined, then form the mixture into 12 evenly sized meatballs. Set aside.
Heat a skillet over medium heat and add 2 tablespoons of butter along with the extra virgin olive oil. Add the shiitake mushrooms, onions, and remaining garlic, cooking until the onions are caramelized and lightly browned, about 8–10 minutes. Remove the mushroom and onion mixture from the skillet and set aside.
Add the venison meatballs to the same skillet and cook, turning as needed, until browned on all sides, about 8–10 minutes. Remove the meatballs and set aside.
Add the remaining butter and flour to the skillet, stirring to form a paste. Slowly pour in the beef broth while stirring continuously to create a smooth, thin gravy. Reduce the heat to low and continue stirring until the gravy begins to thicken.
Return the meatballs to the skillet along with the mushroom and onion mixture. Continue cooking for 8–10 minutes, or until the meatballs are cooked through. Season with salt and pepper to taste and garnish with fresh parsley before serving.