Preheat oven to 400 degrees. Wash the mushrooms, remove the stems and set the mushroom caps aside.

Chop the mushroom stems, onion and garlic.

Over medium heat, warm the olive oil in a medium-sized skillet. Add the mushroom stems, onion and garlic and sauté. One tablespoon at a time, add the red wine, making sure the wine is absorbed by the ingredients and evaporates before adding the next tablespoon. This process should take roughly 10 to 12 minutes, until onion is soft. Add the paprika, thyme, salt and pepper.

Add the ground elk meat and the chopped spinach at the same time. Cook just until spinach leaves have wilted and the meat is brown but not cooked all the way through. Remove skillet from heat.

Using a spoon, scoop the elk meat mixture into the portabella mushrooms; Mushrooms can be stuffed to overflowing if desired. Place thin slices of goat cheese Over the stuffed mushrooms and bake in the oven for 15 minutes, until the cheese begins to turn golden brown and juices are seeping out of mushrooms. Allow mushrooms to sit a couple of minutes before placing on a platter to serve.