Heat the oven to 350°F. Soak the fermented black beans in the vinegar until slightly plumped, 10 to 15 minutes. Add the tahini, nutritional yeast, and a pinch of salt and mash with a fork. Stir the mixture into the vegan mayonnaise to give it the look and consistency of blue cheese dressing. Taste and adjust the seasoning.
Peel the celery root with a sharp knife, and cut into sticks about 1/2 inch wide and 3 to 4 inches long. Whisk the flour, cornstarch, 2/3 cup water, 1/4 cup hot sauce, and a pinch of salt and pepper in a large bowl until no lumps remain. Add the celery root to the batter and toss to coat thoroughly.
Put 1/2 inch oil in a large skillet over medium-high heat. When it’s hot (a drop of batter should sizzle enthusiastically), lift the celery root from the bowl 1 piece at a time, letting any excess batter drip off, and add to the skillet, cooking just a few pieces at a time. Cook, turning once or twice and adjusting the heat to prevent burning until the celery root is golden brown on all sides, 5 to 10 minutes total. Transfer the pieces to a baking sheet in a single layer as you cook additional batches, adding more oil to the skillet as necessary to maintain the depth.
When all the pieces are fried, roast in the oven without turning until the outside is crisp and browned in spots and the inside is tender, 8 to 12 minutes. Drizzle the remaining 1/4 cup hot sauce in a spiral into the dressing and serve with the hot celery root.