Pre-heat a large dutch oven or pot with a lid to medium-high heat. Season the short ribs with salt and pepper, add a splash of oil to the pan, then sear on all four sides until golden brown and crispy, about two minutes on each side. Remove the short ribs from the pan and set aside.
Turn the heat down to medium and saute the carrots, onions and garlic until soft, no need to caramelize. Stir in the tomato paste, cook for 2 minutes, then deglaze with the wine. Let the wine reduce by half.
Add the short ribs back into the pan along with the chicken stock and thyme. The short ribs should be covered about 2/3 with the liquid in the pot, depending on the size of your pot you may need to add more chicken stock. Bring everything to a simmer then cover.
Let the ribs gently simmer on the stovetop, or in a preheated 350-degree oven for 3-4 hours. I like to check them every hour or so, stirring the bottom of the pot to ensure the braising liquid isn't scorching. Use a ladle to skim excess fat that forms at the surface. You will know they are done when the bones are falling out and the meat is fork-tender.
When the ribs are done remove them from the pot and set aside until they are cool enough to handle them. At this point, I like to buzz the sauce with an immersion blender, or you can use a potato masher, just to break up the carrots and onions a bit, this step is optional. Remove and discard the bones, then shred the meat with your hands or two forks and add it back into the braising liquid.
When adding the mascarpone you want to temper it into the sauce. To do this, take a ladle full of sauce and put it into a small bowl. Stir the mascarpone into the bowl then add it all back into the pot. This will ensure that the mascarpone doesn't split or curdle in the ragu.
Lastly, add the cooked pappardelle to the pan and toss it with the ragu. Serve immediately with lots of shaved parmesan on top.