Preheat oven to 325F.
In a small bowl, combine the ingredients for the flax egg and let gel for about 10 minutes.
In a food processor, blitz onion, carrot, and celery until you get a uniform mince.
In a large pan/pot over medium heat, melt the vegan butter and add the onion, carrot, and celery mixture to cook until softened (about 6-7 minutes). Add the garlic and cook until fragrant (1-2 minutes).
Once the veggies have softened, add the dried herbs (sage, thyme, and parsley) to the pan and stir to rehyrdate the herbs.
Add the flax egg mixture and vegetable broth (if you don't like a soggy/homogenous stuffing, start with 3 1/4 cups and add more as needed) and stir to mix everything.
Bring to a simmer and then add the stuffing croutons. Stir to coat and absorb the liquid into the bread. Add salt and pepper to taste.
Transfer to a greased baking dish (I used a 9x13 sized casserole dish) and dot with a couple extra bits of butter for extra richness. You can leave this out but it does help brown it a bit more.
Bake for 30 minutes or until the top is golden.