Pat the venison dry and season generously with salt and pepper. Heat the olive oil in a large, heavy-based casserole over a high heat and brown the meat in two batches until deeply golden on all sides. Transfer to a plate.
Reduce the heat to medium, add the butter and soften the onion, carrots and celery for 10 minutes, stirring often, until sweet and golden. Add the garlic and tomato purée and cook for 2 minutes more.
Pour in the red wine, scraping up all the sticky bits from the base of the pan, and let it bubble until reduced by half.
Return the venison to the pan with the chopped tomatoes, stock, juniper, bay and rosemary. Bring to a gentle simmer, cover and cook on the lowest heat on the hob (or in the oven at 150°C / 130°C fan) for 2 to 2½ hours, stirring now and then, until the meat is completely tender.
Remove the bay leaves and rosemary stalks. Use two forks to break the venison into rough shreds, then simmer uncovered for 10 to 15 minutes until the sauce is thick and glossy. Taste and adjust the seasoning.
Cook the pappardelle in well-salted boiling water until al dente, reserving a mug of the cooking water. Toss the pasta through the ragù, loosening with a splash of the reserved water if needed. Serve topped with Parmesan and parsley.