Recipe source: https://www.mindbodygreen.com/0-12119/a-homemade-vegan-mayo-recipe-that-will-blow-your-mind.html (modified)

0.25 c soy milk
0.25 tsp salt
0.5 tsp dry mustard
1 tsp garlic powder
1 tsp apple cider vinegar
1 tsp maple syrup
0.5 c olive oil

Blend everything except oil in the blender - start on low, then turn it to high.
Add a bit of oil and blend, and keep doing that.  Then, with the blender running, open the top of the blender and slowly pour in the oil.
Keep blending until it's smooth.