Drain and rinse the tofu: Very gently drain the tofu and rinse under running water. It's fine if it breaks while you're rinsing. Transfer the tofu to a blender, food processor, or the cup of an immersion blender.
Combine the mayo ingredients: Add the oil, vinegar, and salt to the tofu. Start with the lesser of the recommended amounts; you can add more to taste later on.
Blend until smooth and creamy: Blend the tofu continuously until it becomes smooth and very creamy. Stop the blender and scrape down the sides as needed during blending.
Taste and adjust: Taste the mayonnaise. Add more olive oil for a creamier, richer mayo or a tablespoon of water to loosen the texture. Add mustard or agave, additional lemon juice or vinegar, or more salt, according to your taste.
Use or store the mayo: Store the mayonnaise in the refrigerator for up to one week.
