How to Make It
Put the venison in a large resealable plastic bag. Add the pure olive oil, 2 tablespoons of the parsley, 1 tablespoon of the pimentón, the garlic and 1/2 teaspoon of salt. Seal the bag and turn to evenly coat the meat. Let marinate for 20 minutes.
Heat the extra-virgin olive oil in a large skillet. Add the onion, cover and cook over moderate heat until translucent, 2 minutes. Add the mushrooms, cover and cook, stirring often, until tender, about 5 minutes. Stir in the remaining 1/2 teaspoon of pimentón. Season with salt. Add the wine; bring to a simmer. Cover partially and cook over low heat until the mushrooms are tender and almost dry, about 6 minutes. Stir in the remaining 2 tablespoons of parsley and keep warm.
Preheat the broiler or heat a grill pan. Thread the venison onto 4 skewers and broil or grill the meat, turning to brown all sides, 3 to 4 minutes for medium rare. Serve with the mushrooms.
Spanish paprika, or pimentón, is available in many styles, sweet being the most common. The smoky pimentón from La Vera, in the Cáceres region, is ground from dried red peppers smoked over oak.