Preheat the oven to 350 degrees(F).
Cut the bread into cubes and then spread out evenly on a large sheet pan.
Toast in the oven for 10-15 minutes or until they are firm and a little crunchy. Set aside, but leave the oven on.
While you toast the bread, get started on the onions. Heat the vegan butter and olive oil on medium high in a large pot.
Add the onions, sauté for a few minutes, until the onions are translucent, then reduce heat to medium low.
Add the garlic, thyme and sugar. Then a pinch of salt and pepper. Stir to combine.
Continue to sauté the onions, spreading the onions out in the pot for a few minutes, then stirring and spreading back out until the onions are nicely caramelized and golden brown. This will take about 30 minutes.
Remove the sprigs of thyme, then pour the vegan beef broth into the pot. Stir to combine.
Bring to a simmer, taste the broth and add salt and pepper as needed.
Now, pour the bread cubes into the pot. Turn off the heat and fold the bread into the broth making sure the bread has all soaked in the broth. Add a little more broth if you have dry bread left.
Pour the stuffing into a 9x9 inch or 13x9 inch baking dish. Cover the top with the vegan mozzarella. Bake for 15-20 minutes.