Heat olive oil in a large Dutch oven over medium-high heat. Season short ribs with salt and pepper and sear on all sides until browned, about 10 minutes. Remove and set aside.
Add chopped onion, carrots, and celery to the pot. Sauté until softened, about 5-7 minutes. Add minced garlic and cook for 1 more minute.
Stir in tomato paste and cook for 2-3 minutes. Add crushed tomatoes and beef broth, mixing well.
Add thyme, rosemary, and bay leaf. Return the short ribs to the pot, cover, and reduce heat to low. Braise for 3-4 hours until the meat is tender.
Once tender, shred the meat and mix it back into the sauce. Adjust seasoning with salt and pepper as needed.
For the mashed potatoes, boil chopped russet potatoes in salted water until fork-tender. Drain, then return to the pot with butter, milk, and Parmesan. Mash until smooth and season with salt and pepper.
Serve the ragu over a generous portion of mashed potatoes, garnished with fresh parsley if desired.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3 days. Reheat gently on the stovetop.