Season each short rib generously with salt. Coat a pot large enough to accommodate all the meat and vegetables with olive oil and bring to a high heat. Add the short ribs to the pan and brown very well, about 2 to 3 minutes per side. Do not overcrowd pan. Cook in batches, if necessary.
Preheat the oven to 375 degrees F.
While the short ribs are browning, puree all the vegetables and garlic in the food processor until it forms a coarse paste. When the short ribs are very brown on all sides, remove them from the pan. Drain the fat, coat the bottom of same pan with fresh oil and add the pureed vegetables and the brown sugar, season the vegetables generously with salt and brown until they are very dark and a crud has formed on the bottom of the pan, approximately 5 to 7 minutes. Scrape the crud and let it reform. Scrape the crud again and add the tomato paste. Brown the tomato paste for 4 to 5 minutes. Add the wine and scrape the bottom of the pan. Lower the heat if things start to burn. Reduce the mixture by half.
Return the short ribs to the pan and add 2 cups water or until the water has just about covered the meat. Add the thyme bundle and bay leaves. Cover the pan and place in the preheated oven for 3 hours. Check periodically during the cooking process and add more water, if needed. Turn the ribs over halfway through the cooking time. Remove the lid during the last 20 minutes of cooking to let things get nice and brown and to let the sauce reduce. When done the meat should be very tender but not falling apart. Reserve the braising liquid, add soy sauce and hoisin sauce to it, simmer for 5 minutes and add the cornstarch (in a slurry) to thicken it up.
For the Noodles:
Boil noodles in lightly salted water until 'al dente', veering on the side of undercooked (you will be stir-frying them later so avoid overcooking them now). Drain and rinse with cold water to prevent sticking. Set aside.
Heat a wok or large frying pan over medium-high heat. Add oil and swirl around, then stir-fry the garlic, ginger, and shallot/onion 1 minute.
Add the short rib in shredded large chunks, the carrots plus 1-2 tablespoons of the noodle sauce you made earlier - enough to keep ingredients frying nicely. Stir-fry 2 minutes, until carrots soften slightly.
Add the mushrooms, broccoli, and red pepper, plus 3-4 more tablespoons of the short rib sauce sauce. Continue stir-frying until mushrooms and red pepper soften and broccoli turns bright green but is still crisp (3-4 minutes).
Now add the noodles plus remaining sauce. Using 2 utensils, lift and turn the noodles in the pan to combine with the vegetables. Stir-fry in this way 3-5 more minutes, or until you are happy with the softness/texture of the noodles. During the last 1 minute of cooking time, fold in the bean sprouts.
Serve immediately in bowls or plates, topping with a sprinkling of fresh coriander or basil. More fresh bean sprouts can also be added as a topping.
Recipe courtesy of Chef Geronimo Lopez with Botika.