Bring a large pot of cold water to a boil. Add the octopus, bay leaf, the quartered yellow onions and salt. Simmer for 2 1/2 to 3 hours. The octopus is ready when a skewer easily pierces and goes through a tentacle.
Remove the octopus from the pot and let it cool down.
Chop the red onions in 12 pieces each. Cut the octopus in 1 inch pieces.
On a barbecue set to medium, grill the octopus just enough to leave grill marks.
Place red onions in a plate. Put the grilled octopus atop the onions, drizzle the olive oil and the white balsamic vinegar over the onion and the grilled octopus.