Peel the onions. Bring water to boil in a large pot, add the peeled onions, and blanch for 1 minute. Drain and rinse in cold water until cool. Press each onion out of its skin.
Peel the carrots and cut them diagonally into thick slices.
Season the beef with salt and pepper on all sides.
Heat the olive oil in a roasting pan over medium-high heat. Working in 2-3 batches, sear the beef for 3-4 minutes per batch until browned on all sides. Transfer all browned beef to a plate.
If needed, add a splash more olive oil to the pan. Add the blanched onions and carrot slices and sauté over medium heat for 5 minutes until they begin to soften.
Add the tomato paste to the vegetables and stir constantly for 2 minutes to lightly toast it.
Pour in the balsamic vinegar and scrape up any browned bits stuck to the pan bottom. Simmer over medium heat for 5 minutes until slightly reduced.
Return the seared beef to the pan. Pour in the meat broth and add the rosemary sprigs. Cover the pan, reduce heat to low, and braise for 2 to 2.5 hours, stirring occasionally, until the beef is very tender.
About 15 minutes before the ragout is done, combine the Marsala and red wine in a separate small saucepan. Bring to a simmer over medium heat and reduce by half, about 10-15 minutes.
Pour the reduced wine mixture into the ragout and stir well. Taste and add more salt and pepper if needed.
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