Line a baking tray with parchment paper. Lay tempeh on a cutting board horizontally and cut into three equal pieces. Take each piece and carefully slice it in half, widthwise, making thin cutlets. Slice each diagonally to make triangle-shaped cutlets. Place water and tamari in a small pot over medium heat. Add the tempeh and simmer for 10 minutes. This important step ensures that the firm tempeh “blooms” or opens up and gets infused with flavor. When done, remove tempeh from liquid and lay on a paper towel to dry. Discard the liquid.
Heat 2 tablespoons of the oil in a large pan. Arrange tempeh in a single layer in the pan with enough room to flip the pieces over. Do this in two batches if necessary. Fry on medium-high heat until browned, about 3 minutes per side. Remove cutlets from pan and set aside.
Reduce heat and add the remaining 2 tablespoons of oil and the vegan butter. Swirl the butter to melt. Add the onion and salt. Cook until soft and translucent, about 8 minutes. Add garlic and cook a few minutes more, being careful not to brown the garlic. Add the broth and let simmer for a few minutes.
In a small bowl, stir together the cornstarch and a couple of tablespoons of hot broth from the pan to make a slurry. When the cornstarch is dissolved, drizzle it back into the pan while whisking with a fork or wire whisk. Add the lemon juice and capers, and continue to whisk until sauce has thickened. Transfer tempeh back into the pan and cover with sauce. Let simmer gently for a few minutes until the tempeh picks up the flavors of the sauce and is heated through. Remove pan from heat and sprinkle with parsley. Serve immediately.