Prepare the pork: Heat butter and olive oil in a Dutch oven over medium heat. Brown the pork on all sides, then remove and set aside.
In the same pot, sauté the onion until soft, then add the garlic and cook for 1 minute.
Deglaze with the Belgian ale, scraping up any browned bits. Stir in the beef stock, Dijon mustard, brown sugar, bay leaves, thyme, salt, and pepper.
Return the pork to the pot, cover, and let simmer on low heat for about 1.5 to 2 hours, until tender.
Prepare the braised leeks: Melt butter in a pan, add leeks cut-side down, and cook until lightly golden. Add vegetable broth and vinegar, cover, and simmer for 15 minutes until tender.
Make the mash: Boil potatoes, parsnips, and carrots in salted water until soft. Drain and mash with butter, milk, salt, and pepper until smooth.
Serve the beer-braised pork with the braised leeks and root vegetable mash on the side.