Combine the water, vinegar, half of the garlic, 1 teaspoon of the oregano, and 1/4 teaspoon of the pepper flakes in a 1-gallon zipper-lock bag. Add the tempeh, press out the air, seal, and toss gently to coat. Refrigerate for at least 1 hour or up to 24 hours, flipping the bag occasionally to ensure even marination.

Pulse the parsley, olive oil, remaining vinegar, remaining garlic, remaining oregano, remaining pepper flakes, and salt in a food processor until the mixture is coarsely chopped, about 10 pulses. Transfer the sauce to a bowl and season with salt and pepper to taste.

Remove the tempeh from the marinade and pat it very dry with paper towels to ensure it browns properly. Heat 2 tablespoons of the vegetable oil in a 12-inch nonstick skillet over medium heat until the oil is shimmering but not smoking.

Add half of the tempeh to the skillet and cook until the first side is deeply golden brown, about 2 to 4 minutes.

Flip the tempeh, reduce the heat to medium-low, and continue to cook until the second side is golden and the centers are hot, another 2 to 4 minutes. Transfer the first batch to a platter, wipe out the skillet with paper towels, and repeat the process with the remaining oil and tempeh.

Serve the warm tempeh immediately with the parsley sauce spooned over the top.