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Blend the tofu, milk, flour, nutritional yeast, salt, turmeric, black pepper, and garlic in a blender or food processor into a smooth, thick batter, scraping down the sides as needed. Taste and adjust the seasoning, if needed, with salt and pepper.
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Preheat a large non-stick skillet or well-seasoned cast iron skillet over medium heat. Spray the pan with oil or spread with a small amount of olive oil.
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Pour 1/2 cup of the batter into the pan. Use a spatula to spread it to about 1/4-inch thick. If you accidentally scrape up some batter, just spread it back.
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Cook the omelet until the surface looks dull and very dry, about 4 minutes. Lift up a corner and check if it has brown flecks all over the bottom side, including the center. Flip the omelet with a spatula when it is no longer sticking to the pan. Cook the other side the same way, about 2 minutes. Push down on the omelet with a spatula to cook the inside. Sprinkle with black salt, if using.
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Optional fillings: If adding cheese, sprinkle the omelet with the cheese, fold in half, cover the pan, and cook on low until the cheese melts. If adding vegetables, repeat the same procedure, but cook the omelet only until the vegetables are heated through. Serve hot.