Peel and dice the carrot. Dice the celery. Peel and dice the onion. Peel and mince the garlic. Trim the oyster mushrooms by removing just the tough, woody ends, about ½ inch. Halve the green beans.
Add just 3 tbsp flour to a large plate with a pinch of pepper and toss the mushrooms in it. Place a large nonstick skillet over medium-high heat with 2 tbsp vegetable oil.
Once the oil is hot, add the mushrooms, in a single layer, and cook until lightly browned and crispy, about 2 to 3 minutes per side. Transfer the crispy mushrooms to a paper towel-lined plate and sprinkle with salt. Cover to keep warm.
Return the skillet to medium heat (no need to wipe it clean) and add the diced carrot, diced celery, diced onion, minced garlic, and a pinch of salt and pepper. Cook, stirring occasionally until softened, about 4 to 5 minutes.
Add the bouillon cube, coconut milk, dried thyme, and 1 cup water. Bring to a boil, reduce heat to low and cook until slightly thickened, about 4 to 6 minutes.
In a large bowl, mix together the remaining flour, baking soda, and ¼ cup water. Mix with a fork until well combined, and use a tablespoon to drop balls of the dumpling mixture into the simmering sauce. Simmer until the dumplings are firm, about 4 to 5 minutes.
Add the green beans and butter to the chick’n and dumplings and stir gently. Cook until crisp-tender, about 1 minute. Taste and adjust the seasoning with salt and pepper.
Scoop the chick’n and dumplings into large shallow bowls and top with the crispy oyster mushrooms.