In a large nonstick skillet, melt butter in the olive oil over medium-low heat.
Add onions and brown sugar then cook until soft, translucent, and becoming golden brown, about 10-15 minutes.
Add broth and cook until onions are deeply caramelized, tender, and sweet, about another 20 minutes. Make sure to stir occasionally to ensure no burned onions.
When onions are done, remove them from the heat and let cool.
In a large medium mixing bowl, mix the sour cream and cream cheese together until smooth, then add cooled onions, garlic, and worcestershire sauce. Stir all ingredients well, taste, and adjust seasoning with salt and pepper.
Cover tightly with plastic wrap and keep in the refrigerator until time to serve.
To serve, stir well and garnish with parsley.