Season flour with salt and pepper in a large bowl.
Dust each cube of meat thoroughly with the seasoned flour. Set aside.
Melt beef tallow or another fat in a large heavy-bottomed Dutch oven over medium heat.
Brown the meat in the fat. This process will take approximately 2-3 minutes until the cubes take on a golden brown color. (See video.) Do this in batches. Do not crowd the meat.
Once all the meat is browned, return all the browned meat to the Dutch oven and pour in the wine, fortified wine, juice, or vinegar water. (See the list of ingredients.) Deglaze the bottom of the Dutch oven.
Next, add the bone broth, broth, or water to the Dutch oven. Also, add in the bay leaves. Stir well and bring the mixture up to a boil. Cover the Dutch oven, turn the heat down to low, and allow the meat to simmer for 1 1/2 hours.
After 1 1/2 hours, remove the lid from the Dutch oven. Add the carrots, potatoes, and mushrooms to the Dutch oven. Stir well.
If you are using large onions that have been quartered instead of pearl onions, add these to the mixture at the same time you add the carrots, potatoes, and mushrooms.
Bring the mixture up to a boil, and return the lid to the Dutch oven. Turn the heat down to medium-low, and allow the mixture to simmer for 30 minutes.
After 30 minutes of allowing the vegetables to simmer along with the meat, remove the lid from the Dutch oven.
Mix the 1 tablespoon of flour with the butter to form a ball. Add this ball to the stew and raise the heat to bring the mixture up to a boil, stirring constantly as the ball melts and thickens the stew. (See video.)
Once the stew has thickened, lower the heat to medium and add the pearl onions and the peas. Stir well. The stew is done once the onions and peas are warmed through.
Once warmed, the stew is ready to serve. If you want, place the egg noodles in a bowl and ladle the stew on top of the egg noodles. Top with a bit of chopped fresh parsley. Alternatively, you could serve the stew with thick slices of sourdough bread.
Leftovers will stay fresh in the refrigerator for 3-4 days or up to 3 months in the freezer.