Simmer tempeh (optional): Simmer the tempeh in water to cover by 2 inches for 3 minutes to remove the slightly bitter flavor before crumbling. Run the block under cold water. Use your hands to break the tempeh into crumbles.
Sauté tempeh: Heat 2 teaspoons olive oil over medium-high heat in a large nonstick skillet. Cook the tempeh crumbles, if using, for about 5 minutes until golden brown, stirring occasionally. Add 1 tablespoon soy sauce and cook for 1 minute more, stirring constantly. Transfer to a bowl and set aside.
Cook mushrooms: Add a drizzle of olive oil to the same skillet and heat over medium-high heat. Cook the mushrooms for about 6 minutes, or until they release their liquid and brown, stirring occasionally. Transfer to the bowl with the tempeh, if using, and set aside.
Cook onion, carrots, and garlic: Drizzle more olive oil into the same skillet. Cook the onion, carrots, and garlic for about 5 minutes, or until the onions are translucent. Add the flour and cook for 2 minutes more, stirring constantly.
Add liquid: Whisk in the vegetable broth and lemon juice.
Add the potatoes, bay leaves, rosemary, thyme, oregano, and basil. Bring the liquid to a gentle boil before reducing the heat to a low simmer. Simmer with the lid on for about 15 minutes, or until the potatoes are fork tender, stirring occasionally, and adding more broth as needed to keep the vegetables submerged.
Combine ingredients and season: Discard the bay leaves. Add the tempeh crumbles (if using), beans, peas, and coconut milk. Add more water or broth as needed until the desired consistency. Season with salt and pepper. Adjust soy sauce and lemon juice to taste.
Garnish with fresh parsley.