ROOT BEER-BRAISED SHORT RIBS

Steps:

• Trim the short ribs of any fat, sinew, and connective tissue. While cleaning the meat, reserve all the trimmings in one pile (for the sauce) and the cleaned ribs in another. Lay the short ribs together, arranging them in two stacks, each in a double layer. Use butcher's twine to tie the pieces together, starting at one end and placing each tie about 1 1/2 inches (3.75 centimeters) from the previous one.
• Set up an ice bath.
• In a small pot set over high heat, bring 2 cups (450 grams) of the water to a simmer. Add the birch bark, turn off the heat, and cover the pot for 15 minutes. Strain the birch bark from the water and pour into a medium-sized metal bowl. Combine with the remaining 4 1/2 cups (1,012.5 grams) water, the sugar, salt, and vanilla. Chill the brine in the ice bath.
• Place the short ribs in 2 separate zip-top bags and cover them with the cooled brine. Seal the ribs in the bags with the brine and refrigerate them for 24 hours.
• Measure out approximately 1 1/2 pounds (670 grams) of the reserved short rib trim. Put the trimmings, 3 1/3 cups (787.5 grams) water, the root beer, onion, wine, ketchup, and garlic in a pressure cooker and cook on high pressure for 1 hour. Let the pressure dissipate naturally. Strain the sauce, discarding the solids, let it cool to room temperature, and refrigerate for at least 2 hours.
• Preheat a circulating water bath or a large pot of water on the stove to 149°F (65°C).
• Skim off the layer of fat that has solidified on top of the sauce and discard.
• Remove the short ribs from the brine. Pat them dry and place them in 2 vacuum-seal bags. Add equal amounts of the root beer sauce to each bag and seal shut. Alternatively, you can seal them in zip-top bags, removing as much air as possible. (You may want to use a double layer of bags to avoid any leaks.) Place the bags in the water bath and cook for 24 hours (using a large pot over low heat to maintain the temperature). Set up an ice water bath and transfer the bags to it so they can cool off quickly.
• When the ribs are cool, remove them from the bag and strain the cooking liquid.
• Divide the cooking liquid in half. Pour half into a pressure cooker and add the carrots. Reserve the other half for sauce. Cook on high pressure for 3 minutes. Let the pressure dissipate naturally. Let the carrots cool in the liquid. Alternatively, simmer the carrots in the liquid until tender and let them cool down naturally. When the carrots are cool, cut them into oblique shapes and reserve them in the cooking liquid.
• To serve, preheat a circulating water bath or a large pot of water on the stove to 140°F (60°C). Put the short ribs and reserved liquid in either vacuum bags or zip-top bags, making sure to remove any excess air, and cook for 10 to 15 minutes until heated through.
• While the short ribs warm up, heat the carrots and their reserved liquid in a separate pot set over medium heat.
• Place a large cast-iron or other heavy-bottomed skillet over medium-high heat. When the ribs are warm, remove them from the bag, straining the liquid into a small pot, and brown them briefly on each side in the skillet. Keep the sauce warm on low heat. Transfer the ribs to a cutting board. Slice the ribs and divide among 4 plates. Add the carrots and pour the root beer sauce over all.