Arrange oven rack to accommodate a Dutch oven in the relative center of the oven. Preheat oven to 300 degrees F.

Heat 1 tablespoon oil over high heat in a large heavy bottom, oven-safe Dutch oven. Sprinkle ½ teaspoon salt and pepper to taste over venison. Add half of venison to the hot oil in a single layer and let sear, undisturbed until browned on the bottom, 2 to 4 minutes. Turn pieces of the meat over with tongs, and let sear on a second side, 2 to 4 more minutes. Transfer the meat to a plate. Reduce heat to medium-high, add the remaining 1 tablespoon of to the Dutch oven and repeat searing the remaining venison. Transfer it to the plate.

Reduce heat to medium. Add garlic, onions and mushrooms and cook, stirring often until the onions start to brown and the mushrooms have released their juices and the juices have started to evaporate, 5 to 7 minutes. Add in oregano, thyme, paprika, the remaining 1 teaspoon salt and more pepper to taste. Cook stirring until the spices are fragrant, 30 seconds to 1 minute.

Add red wine to the Dutch oven, increase heat to high, and simmer until it is almost completely evaporated, about 2 minutes. Add broth and tomato paste and bring to a simmer, stirring often to dissolve the tomato paste into the broth. Once the stew comes to a simmer, add in the venison and juices from the plate, carrots and potatoes (or root vegetables) and return to a simmer.

Cover the Dutch oven and transfer to the oven. Bake until the venison is completely tender, about 3 hours 45 minutes.

Mash the butter with flour in a small bowl until completely smooth.

Set the stew on the stovetop, remove lid and set heat at medium. Whisk about ¾ of the butter mixture into the stew and bring to a simmer. If the stew seems thin or watery, add the remaining butter and flour mixture and stir until it is melted into the stew. Simmer until the starch thickens.

Stir in peas. Serve with parsley on top if using.