Combine stock, tomato paste, fish sauce, gelatin, soy sauce, and Worcestershire sauce in a blender and blend until mixed. Set aside. Adjust oven rack to lowest position and preheat oven to 300°F (150°C).
In a large Dutch oven, heat oil over medium-high heat until shimmering. Season beef all over with salt and pepper and add to Dutch oven. Cook, turning occasionally, until beef is well browned, about 10 minutes. Transfer beef to a mixing bowl and set aside.
Add mushrooms to Dutch oven and cook, stirring, until liquid is released and mushrooms begin to brown, about 6 minutes, lowering heat as necessary to prevent scorching. Add diced carrots and shallots and cook, stirring, until well browned on all sides. Season to taste with salt and pepper, transfer to a mixing bowl, and set aside.
Add halved yellow onion to Dutch oven, cut side down. Add whole carrots, celery stalks, and garlic. Cook, turning carrots, celery, and garlic occasionally until all the vegetables are well-browned, about 8 minutes.
Add the sherry, scrape up browned bits, and cook until reduced by 3/4, about 3 minutes. Add broth mixture and bring to a simmer. Remove from heat.
Add the stew meat to a large bowl and toss with the flour. Add beef and any juices accumulated in the mixing bowl to the Dutch oven, along with bay leaves and thyme sprigs. Stir to combine and return to a simmer over medium heat. Transfer to oven, cover with lid partially open, and cook until beef becomes tender, about 1 1/2 hours. Watch the stock level and add more if needed. Adjust oven temperature if necessary during cooking. Remove stew from the oven, and using tongs, remove and discard the carrot, celery, thyme, bay leaves, onion, and garlic. Add the potatoes, reserved sautéed mushrooms, shallots, and carrots to the stew, return to oven, and continue to cook, partially covered, until beef, potatoes, and carrots are tender and the broth has thickened 45 minutes. Remove stew from oven, and if necessary, place over a burner and simmer for up to 15 minutes to reduce to desired consistency. Stir in frozen peas, carrots, and corn. Season to taste with salt and pepper if necessary.
Make the Dumplings
Combine the flour, baking powder, parsley, 1 tsp salt, and 1 tsp pepper in a large mixing bowl.
Place milk and butter in a bowl and microwave until the butter is melted.
Add the milk mixture to the flour and mix until well combined.
Add golf ball-sized potions of the dumplings to the stew. There should be about 15 dumplings. Simmer covered for about 20 minutes or until the center of the dumplings is done.
Serve immediately. It can be stored refrigerated for five days.