Marinating the tempeh (you can do this first before you prep everything else or the day before for maximum absorption and flavor):
Cut the block of tempeh in half width wise so it makes two shorter blocks.
Boil or steam in a pot of water for about 20 minutes. This cuts the bitterness from the tempeh.
Meanwhile, make marinade by combining everything in a large container or large ziplock bag.
Once the tempeh is done, allow to cool. Then cut into thin slices, about 1/8 inch thick. Using a very sharp knife will make this easier.
Add thinly sliced tempeh into the marinade and allow it to soak for at least 4-6 hours, overnight is best. If using mushrooms then put thin slices right into marinade.
Once tempeh is ready:
Preheat oven to 350 F (175 C).
Take tempeh slices out of the marinade (save it!) and spread them out in a thin layer in a 9 x 13 baking dish. Do this with mushroom slices too but no need to save the marinade.
Gently pour about 1/4 cup of the marinade over the tempeh slices.
Bake for 30-35 minutes or until the edges are brown.
Meanwhile, if you are making the potatoes, slice the potatoes into thick french fry sized slices. I keep the skins on but you can peel them if you prefer.
Place them in a bowl and cover with water to help remove some of the starch. Allow to soak for 5-10 minutes. A trick I use, is that I marinade the tempeh/potatoes in a plastic bag. Then I drain the bag and use it to put potatoes in with other ingredients so that they get some of the flavorings.
Prep the tomatoes, red onion, lettuce and make tzatziki if you haven't yet.
Drain the potatoes and pat dry. Put them back in the bowl.
Add broth or oil and salt. Mix well.
Once tempeh gyro slices are done, remove from oven and cover with foil to keep warm. Set aside.
Turn the oven up to 450 F (230 C).
Spread the potatoes over a cookie sheet and bake for 30 minutes.
When the potatoes are done, warm the pita bread in a damp towel for 2-3 minutes to soften.
Build your gyros with the tempeh gyro slices, potatoes, tomatoes, red onion and lettuce if preferred.
Drizzle tzatziki over the top and devour!
Another option for the potatoes is using aquafaba if you don't use oil. Aquafaba is simply the juice from a can of chickpeas. Use the same amount as the broth.
Adjust the amount of salt based on your taste. You may need more or less depending on what broth and Tamari/soy sauce you use.
You can substitute garlic powder for fresh garlic if you don't have it, but the fresh garlic yields a more authentic flavor.
Nutrition info does not include Tzatziki, see the recipe for the info. It also only takes into account about 1/4 of the marinade since you are not eating the entire marinade.