In a large Dutch oven, heat 1 tablespoon of olive oil over medium-high heat. Season 3-4 pounds of beef short ribs with salt and pepper, then add to the pot. Sear the ribs on all sides for about 10 minutes until they develop a rich, golden-brown crust. Once browned, remove the short ribs and set them aside on a plate.

In the same pot, add one chopped large onion, two peeled and chopped carrots, and two chopped celery stalks. Sauté the mixture for 5-7 minutes until the vegetables soften and become fragrant. Then, stir in two minced garlic cloves, cooking for an additional minute until it becomes aromatic, developing a savory base for your tender short ribs.

Add 1 tablespoon of tomato paste to the vegetable mixture; let it cook for 2-3 minutes to deepen the flavors. Then, pour in 2 cups of crushed tomatoes and 1 cup of beef broth, stirring to combine all the ingredients.

Return the browned short ribs to the Dutch oven, adding 1 teaspoon of dried thyme, 1 teaspoon of dried rosemary, and 1 bay leaf. Cover the pot with a lid, reduce the heat to low, and braise for 3-4 hours.

Once the short ribs are tender, remove them from the pot and let them cool slightly. Use two forks to shred the meat, discarding any bones and excess fat. Return the shredded beef to the sauce, stirring gently to combine. Taste and adjust the seasoning with salt and pepper as needed.

While the ragu simmers, peel and chop 2 pounds of russet potatoes. Place them in a pot of boiling salted water and cook for 15-20 minutes until fork-tender. Drain the potatoes and return them to the pot, adding ½ cup of unsalted butter and ½ cup of milk. Mash the mixture until smooth, and then fold in ½ cup of grated Parmesan cheese.

To serve, spoon a generous portion of the creamy Parmesan mashed potatoes onto each plate. Top them with the savory, tender short rib ragu, optionally garnished with chopped parsley before serving.