Place a large pot over medium heat. Once hot, add in the olive oil and butter.
Once the butter is melted, add the onions, stir, and cook for 5 minutes, stirring occasionally.
Season the onions with the sugar, salt, and pepper, stir, and cook for 2 minutes.
Combine the vegan beef stock and wine in a container.
Add 1/4 cup of the stock/wine blend to the onions, stir well, and let cook for 3 minutes. Stir occasionally. Repeat this exact step multiple times until all the liquid has been added to the onions. This step will take about 30 minutes. *Make sure to check the onions frequently to ensure they are not sticking to the bottom of the pan or burning.
After you've added the last bit of liquid to the onions, continue cooking them for 5 minutes, stirring frequently to prevent them from burning and sticking to the pan.
Add the thyme to the onions, stir, and cook for one minute.
Remove 1/4 cup of the onions and set aside for the breadcrumb topping.
Add the flour to the onions and stir for one minute.
Now add 1/2 cup of the milk at a time, stirring the entire time. Once all the milk has been added, turn the heat down to medium-low, add the mozzarella, and stir until the cheese is completely melted.
Add the cooked noodles to the sauce and stir until evenly combined.