For the braised short ribs: Preheat your oven to 375 degrees F.
In a Dutch oven, add the oil and heat it over medium-high heat. Season both sides of the short ribs with 1 tablespoon salt and 1 1/2 teaspoons pepper, then place them in the hot pot and cook them until brown and crispy, about 3 minutes on each side; work in batches so you don't overcrowd the pot. Remove to a plate and set aside.
Discard all but 1 tablespoon of the oil left in the pot, then add the bacon and cook until crispy, about 4 to 5 minutes; remove to a plate. Discard all but 2 tablespoons of fat. Add the garlic, carrots, celery and onions and saute until softened and the veggies develop some color, 7 to 8 minutes. Stir in the tomato paste and cook for 1 more minute. Add the rosemary, beef broth and wine and put the short ribs and bacon back in, submerging them in the liquid. Cover the pot and pop it in the oven until the meat is tender and easily shredded, 2 1/2 to 3 hours.
Take the short ribs out of the pot and cool them enough so you can handle them. (Keep the oven on.) Skim off as much fat as possible from the sauce, adjust the seasoning to taste and discard the rosemary sprigs.
Using your fingers, shred the short ribs and put the meat back in the pot with the sauce. Set aside.
For the white sauce: In a large saucepan, add the butter and melt it over medium heat. Add the flour and cook, stirring constantly, for about 1 minute. Add the milk, and cook the sauce until it thickens enough to coat the back of a spoon, stirring occasionally, 9 minutes. Season with the nutmeg, 1 teaspoon salt and 1/2 teaspoon pepper. Stir in the shredded cheeses and Parmigiano, and take it off the heat.
For the lasagna: Butter a 9-inch-by-13-inch glass baking dish well.
Ladle 1/2 cup of the sauce in the bottom of the baking dish, then lay 4 lasagna noodles in the bottom of the dish, overlapping a little. Spoon over a couple ladles of the sauce followed by 1/2 cup of the shredded cheese mixture and a good sprinkle of Parmigiano. Layer noodles on top. Continue this process until you end up with the 5th layer of the noodles being the very top; cover them with the remaining sauce. It will look like a lot, but don't worry¿the lasagna noodles will absorb any liquid and the lasagna will compress as it cooks in the oven.
Cover the lasagna with some aluminum foil and bake for about 1 hour. Uncover, sprinkle over the remaining 1/2 cup shredded Italian cheese blend and the remaining grated Parmigiano. Bake, uncovered, until golden brown and bubbly on top, another 20 minutes. Allow to cool 30 minutes before serving.