Begin by making the stew. Coat the bottom of a large pot with 2 tablespoons of oil and place it over medium heat. When the oil is hot, add the mushrooms in an even layer. Avoid crowding the pan and cook them in batches if needed. Allow the mushrooms to cook for about 5 minutes, flip, and cook 5 minutes more until lightly browned on both sides. Remove them from the pot and transfer to a plate.
Add the remaining oil to the pot. When the oil is hot, add the celery, carrot, and onion. Sauté for about 10 minutes, until the veggies begin to soften.
Stir in the garlic and flour. Sauté about 2 minutes more, until the garlic is very fragrant and the flour evenly coats the veggies.
Stir in the stout, broth, tomato paste, cabbage, potato, and thyme. Return the mushrooms to the pot. Raise the heat and bring the liquid to a boil. Lower the heat and allow the mixture to simmer, uncovered, for 10 minutes. The veggies should be a bit firm at this point. You can add up to a cup of water during simmering if the broth reduces too much.
While the stew simmers, make the dumpling dough. Stir the flour, nutritional yeast, baking powder, salt, thyme, and chives together in a medium mixing bowl. Stir in the milk and oil to form a soft and sticky dough. Be careful not to overmix.
After the stew has simmered for 10 minutes, taste-test the broth and season it with salt and pepper to taste. Then drop 2-3 tablespoon dollops of the dough into the stew. Make sure you've got plenty of room, as the dumplings will expand as they cook.
Cover the pot and lower the heat. Allow simmering for about 15 minutes more, until the veggies are tender and the dumplings are fluffy.
Ladle into bowls and serve.