In a medium bowl, mix together the first 4 ingredients (beef through thyme). Form meat into patties.
Heat indoor grill pan or skillet to medium-high heat. Place patties on grill pan and cook for 5 to 8 minutes on each side, or until the burgers are cooked to the desired doneness.
In a large skillet over medium heat, heat olive oil. To the skillet, add the mushrooms and cook for 3 to 5 minutes on each side, until crispy on the outside and tender on the inside, season with salt and pepper.
Layer mushroom cap, burger, avocado, red onion and lettuce and then top with another mushroom cap and serve.