Pat the short ribs dry and season with salt and pepper.

Heat the olive oil in a Dutch oven over medium heat. Sear the short ribs for 3-4 minutes per side. Remove and set aside.

Add the onion, celery, and carrots to the pot. Cook for 5 minutes, stirring occasionally. Add the garlic, dried thyme, and tomato paste. Cook for another 5 minutes, stirring frequently.

Pour in the red wine, scraping up any browned bits from the bottom of the pot. Simmer for 10 minutes.

Stir in the crushed tomatoes and beef stock. Add the rosemary, bay leaves, and short ribs. Cover and bake at 325 for 3 hours, or until the meat is tender.

Remove the bones, rosemary stem, and bay leaves. Shred the meat. Simmer uncovered on low for 15 minutes.

Boil the lasagna noodles in water until slightly undercooked. Drain and set aside.

Melt the butter in a saucepan over medium low heat. Whisk in the flour and cook for 5 minutes, whisking frequently. Gradually whisk in the milk, 1 cup at a time. Cook until thickened, then remove from the heat and stir in the Parmesan. Add salt and pepper to taste.

Increase the oven temperature to 400. Spread a thin layer of the meat sauce across the bottom of a 9x13 baking dish.

Layer noodles, meat sauce, béchamel, and shredded mozzarella. Repeat x 3. Finish with a final layer of noodles, béchamel, mozzarella, and grated Parmesan.

Cover with foil and bake for 40 minutes. Remove the foil and bake for another 15 minutes, until bubbling and golden.

Top with fresh parsley and let rest for 45 minutes before slicing and serving.