For the ribs: In a large Dutch oven or heavy-bottomed stockpot, heat the oil over medium-high heat. Season the ribs with 2 teaspoons salt and 1 teaspoon pepper. Add the ribs to the pan and cook until brown, about 4 minutes each side. Remove the ribs and set aside. Add the onions, garlic, and rosemary. Season with salt and pepper. Cook until the onions are translucent and soft, about 5 minutes. Increase the heat to high. Add the wine and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Add the beef broth and ribs to the pan. Bring the mixture to a boil. Reduce the heat to a simmer, cover the pan, and cook until the meat is very tender , 2 1/2 to 3 hours. Remove the ribs and set aside until cool enough to handle, about 20 minutes. Discard the bones and cooking liquid. Using 2 forks, shred the meat into 2-inch long pieces (to yield approximately 2 1/4 cups shredded meat).
For the filling: In a medium heavy-bottomed saucepan, bring the milk and cream to a simmer over medium heat. Reduce the heat to low. Add the cheeses and whisk until melted and the sauce is smooth. Remove the pan from the heat and stir in the spinach, basil, and garlic. Place the shredded meat in a medium bowl and pour the spinach mixture on top. Add the salt and pepper. Using a fork, mix until combined. Taste and adjust the seasoning with salt and pepper, if needed.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until just tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain and set aside.
Place an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Butter a 9 by 13-inch glass baking dish.
Spread 1 cup marinara sauce in the bottom of the prepared baking dish. Lay 4 noodles flat on a dry work surface. Spread 1/4 to 1/3 cup of the filling mixture evenly along each noodle. Roll up and place seam-side down in the baking dish. Repeat with the remaining noodles and filling to make 12 lasagna rolls. Spoon the remaining marinara sauce on top and sprinkle with Parmesan. Drizzle with olive oil, and bake until the lasagna rolls are heated through and the cheese is beginning to brown, about 25 minutes.
Recipe courtesy of Giada De Laurentiis