Preheat the oven to 330 degrees F.
Season the deer meat with salt and pepper. Coat a large pan with the olive oil and heat over medium-high heat. Once the oil starts to lightly smoke, add the venison and cook on all sides until golden brown. Set the pan and meat aside.
In a blender or food processor, puree all of the vegetables (except the green peas), herbs, and garlic until it looks like a thick paste.
Remove the meat from the pan and heat the pan to medium heat. Add the tomato paste, Worcestershire sauce, and the vegetable puree to the pan and cook for 7-8 minutes while stirring frequently.
Add the red wine and scrape all of the bits off the bottom of the pan. Reduce the mixture by half.
Place the venison in a baking dish or a Dutch oven. Pour the vegetable and wine mixture over the meat. Add about 2 cups of stock or enough to cover the meat about 3/4 of the way. Cover and cook for 3-4 hours or until the meat is fork-tender.
While the venison is cooking, place the potatoes in a pot and cover them with water. Bring to a simmer and cook until fork tender (about 15 minutes)
Strain the potatoes and whip them with an electric mixer along with the melted butter, milk, Parmesan, and salt. If the potatoes are too thick adjust with more milk. Alternatively, you can use a potato masher or potato ricer to process the potatoes and then fold in the remaining ingredients.
When the venison is tender, remove it from the oven and increase the temperature to 400 degrees F.
Remove the venison from the cooking liquid and place it into a large bowl. Shred the meat very finely, adding a little of the cooking liquid to ensure that the meat mixture is moist. Season to taste with salt and ground black pepper.
Add the venison filling and green peas to a casserole dish or individual ramekins. Carefully spread the potatoes on top of the meat, making sure that it is fully covered.
Sprinkle some Parmesan cheese on top and bake for 18-20 minutes or until golden brown. For a little extra color, dust with a little sweet paprika.