Season beef shanks or any braising cut generously on all sides with salt and black pepper. Heat 1 tbsp of butter in a pressure cooker over high heat. Sear each shank one at a time—don't crowd the pan—until deeply browned on both sides. Set aside and repeat with remaining shanks.
Once all shanks are seared, return them all to the pressure cooker. Seal the lid and cook on high pressure for 30 minutes, until the meat is completely fall-off-the-bone tender. Dutch oven method: add a splash of water, cover, and braise at 350°F for 1.5–2 hours, adding water as needed to prevent burning.
Once the pressure has released, remove the shanks and let them cool enough to handle. Shred the meat into bite-sized pieces using two forks, discarding any bones and excess fat. Set aside.
In a large pan, melt the remaining butter over medium heat. Add onion, diced, and sauté until golden and soft, about 5–8 minutes. Add sliced mushrooms, Dijon mustard, and chopped garlic; season with salt and black pepper; and cook on medium heat until the mushrooms are soft and all the liquid has evaporated.
Pour in heavy cream and add chopped fresh dill. If you have a Parmesan rind (optional), drop it in now for extra depth of flavor. Bring to a gentle boil and cook for 5 minutes until the sauce thickens slightly. Discard the parmesan rind. Stir in the ½ cup of grated parmesan cheese and taste for seasoning.
Preheat the oven to 400°F. Slice the top off each of the 4 sourdough bread rounds and carefully scoop out the soft interior, leaving a sturdy shell about an inch thick. Save the bread tops.
Divide the shredded meat between the bread bowls. Spoon the mushroom cream sauce generously over the meat. Top with a heavy handful of grated parmesan.
Place the bread lids back on top. Bake at 400°F for 10–12 minutes until the cheese has melted and the bread is golden and toasted.