Heat a skillet until water droplets steam away when dropped on it.
Add the onions to the skillet and stir until they release their water and begin to brown.
When they begin to stick to the skillet, add 1/4 c water and stir.
Cover with a lid and let cook for 5 minutes stirring occasionally and adding 2 tablespoons of water if they start to stick to the skillet.
Add another 1/4 cup of water, stir and cover with the lid and cook another 5 minutes.
Repeat step 5 one or two more times until the onions are soft.
Add the balsamic vinegar and stir.
Replace the lid, and let cook for another minute or two.
Remove the lid and stir until the liquid is gone.
Remove from heat, sprinkle with a pinch of salt, stir, replace the lid and let sit for 5 minutes.
Remove the lid and stir, spreading the onions over the entire bottom of the pan to cool.
While the onions are cooling, place all of the other ingredients (except the aquafaba) into a food processor fitted with an S-blade.
Process until smooth adding the aquafaba a little at a time as needed to achieve desired texture.
Pulse or stir in 1/4 cup of the cooked onions.
Remove mixture to a bowl and spoon the remaining onions on top.