Source: http://www.pennilessparenting.com/2013/03/homemade-vegan-mayonnaise-recipe-flax.html

Ingredients

1 tablespoon ground golden flax seeds
3 tablespoons water, just off the boil
1/2- 1 1/2 cups olive oil (or 5 tbsp)
1 tbsp fresh Lemon juice
Salt to taste
1 tsp coconut sugar
Pinch of freeze dried ginger
Freeze dried garlic
Pinch of white pepper
Pinch of cayenne pepper

Directions

1. Combine ground flax seeds and boiling water in a container, mix constantly, until thickened. Let cool off until it reaches room temperature or close to it.

2. Add lemon juice and seasoning to the bottom of a glass measuring cup. Add flaxseed egg and one tablespoon of oil. Blend for 15-20 seconds with an immersion blender.

3. Add another tablespoon of oil, and blend for another 15 seconds.

4. Repeat step 3 many times, never adding more than a tablespoon of oil at a time. At some point, usually by the third or fourth tablespoon, the color will become white and opaque, like that of mayonnaise. Keep adding more and more oil until it becomes the texture of mayonnaise.

5. Use as you would any mayonnaise!