Clean mushrooms with a wet paper towel and cut into thin slices. Keep aside. Clean 4-5 sprigs of thyme and either roughly chop or remove leaves from the stems.
Heat a heavy-bottom, wide-mount, shallow pan over medium heat and add 1 tsp of avocado oil. Once the oil is heated, add the finely chopped shallots, minced garlic, and 1/4 (half) tsp salt. Cook for about 2-3 minutes, stirring often.
Once the shallot and garlic have softened, stir in all the walnuts. Add 2 pinches of black pepper. Cook, stirring a few times to prevent the shallot and garlic mixture from sticking, for about 3-4 minutes. The walnuts should be slightly darker than their original color.
Reduce the heat to a low and take out about 1/2 cup shallot, garlic, and walnut mixture from the pan to a blender. Let it cool for five minutes. Then add to it the lemon juice, 2 pinches of salt, 2 pinches of black pepper, and 1/2 cup water. Blend until you have a creamy mixture. Set aside.
While the mixture cools in the blender, add the thinly sliced mushrooms, remaining salt and pepper, and 1 tsp thyme, to the remaining shallot, garlic, and walnut mixture in the pan. Cook mushrooms stirring often for about 5-7 minutes. Add the fresh thyme leaves and stir a couple of times before turning the heat off. Divide the mixture into 8 parts.
When you are ready to eat, Heat a medium-sized iron skillet over medium heat. Smear with oil (or go without the oil) and put the sourdough bread slices directly on the skillet. Let is slowly crips both sides; about 1-2 minutes on each side. Alternatively, you can also crisp the bread without oil in a toaster.
Spread 1 tbsp of blended walnut/shallot/garlic cream over a toast, then add 1/8th of the total mushroom mixture over the creamed toast. Sprinkle the balance of fresh thyme on each toast. Enjoy warm.