Make the flax egg by combining the flax meal and water, set aside.
Process the oat in the food processor to make oat flour, set aside.
Combine the walnuts, mushrooms, onions, and garlic in the food processor and pulse until coarsely chopped.
Heat a non-stick pan over medium heat. Add the mushroom mixture to the pan and cook until most of the water has evaporated and the mixture is browned, about 4 minutes.
Put the mixture in a mixing bowl and let cool for a couple of minutes.
Combine the the walnut mixture, the oat flour and the flax egg together. Fold in the spices, Worcestershire sauce, and liquid smoke. Place this in the fridge to chill for 1 hour.
While the walnut mixture is chilling, sauté the mushrooms and onions for the toppings. Add the vegan butter to a non-stick pan over medium heat, add the mushrooms and onions, a pinch of salt and some pepper. Saute for about 10 minutes or until the onions are caramelized and starting to burn slightly.
You can also prep the other toppings and clean the work area while the mixture is chilling.
Once the mixture is chilled, divide it into four equal parts, and roll them into balls.
Heat a non-stick pan over medium heat, add a small amount of oil and one or two of the balls. Cover it with a piece of parchment paper and press it flat with a spatula (see the pictures above if you need a visual). Remove the parchment paper and cook for about 2 minutes and flip.
Add a piece of the vegan cheese to the top and cook for about 30 seconds. Then add a tbsp of water to the side of the pan, away from the burgers, and immediately cover the pan to trap the seam and help the cheese melt. Keep covered for 1 - 2 minutes and then remove from heat.
Assemble 2 (1 is okay too) of the smash burger patties on hamburger buns with lettuce, tomatoes, vegan mayo, avocado and the sauteed onions and mushrooms.