Preheat your oven to 325°F.
Season the beef short ribs with salt and pepper. Heat a heavy, oven-safe pot over medium-high heat and sear the short ribs on all sides until browned, about 2-3 minutes per side.
Add minced garlic and chopped rosemary to the pot, allowing them to infuse the meat with flavor for about 1 minute.
Add a small amount of water or beef broth (optional, about 1/4 cup) to deglaze the pot, then cover with a lid and transfer to the preheated oven.
Slow-braise the short ribs in the oven for about 2 to 2.5 hours until tender.
While the ribs are braising, prepare the roasted vegetables. Peel and cut the carrot and parsnip into 1-inch pieces, and slice the red onion into wedges.
Toss the vegetables with olive oil, a pinch of salt, and pepper. Spread them evenly on a baking sheet.
Roast the vegetables in a separate oven at 400°F for about 20-25 minutes until tender and slightly caramelized, stirring halfway through.
Once the short ribs are tender, remove them from the oven. Plate a portion (approximately 5 ounces of meat) with a generous serving of roasted vegetables.
Garnish with extra rosemary if desired and serve immediately.