Melt 2 tablespoons of the butter in a pot over medium heat. Stir in vegetable oil.
Add the sliced onions and sauté until well caramelized, at least 10 minutes.
Stir in the flour and remaining 2 tablespoons of butter to create a roux in the pot of onions. Stirring constantly, bring the roux up to a simmer and let cook 2 minutes.
Pour in milk and water and stir to combine with the roux.
Stir in bouillon granules, onion powder, and pepper and bring up to a simmer. Stirring constantly, let simmer 3 minutes, or until slightly thickened
Reduce heat to low and stir in Velveeta cheese. Stirring constantly, leave on the heat just long enough to melt the cheese. Once melted, immediately remove from the heat and serve topped with shredded Cheddar cheese.