Add olive oil to a large skillet. Add onions, stir, and bring to medium heat. Do not stir again for 5 minutes.
Add salt, stir, and turn down heat to medium-low. Cook for about 45 minutes, stirring occasionally, until golden brown and caramelized. They should soft and sweet. Stir in balsamic vinegar and white wine. Bring heat back to medium-high to evaporate liquids. Remove from heat and set aside.
To make dip, add all dip ingredients to a large bowl including 1/2 cup of the walnuts. stir gently to combine. Then add 3/4 of the caramelized onions. Stir to fully incorporate.
To top, add remaining caramelized onions and walnuts to the top. Serve with tortilla chips or potato chips.