Cut the pressed tofu into small chunks and transfer them to the bowl of a food processor fitted with the metal blade. Add the lemon juice, parsley, mustard, and garlic powder and pulse 10 to 15 times. Scrape down the sides of the bowl with a rubber spatula and then pulse for about 15 seconds.
With the food processor running, slowly drizzle the oil through the feed tube into the tofu mixture, blending until it is the consistency of mayonnaise, 2 to 3 minutes. If necessary, thin the tofu with water, 1 teaspoon at a time. Season to taste with salt and pepper, and pulse to mix. Set aside until ready to use, or transfer to a container with a tight-fitting lid and refrigerate for up to 10 days.