In a large saute pan, heat the oil over medium-high heat. Add the onion and cook for 4-5 minutes or until tender. Add the broccoli to the pan and cook for an additional 4-5 minutes. Transfer the veggies to your slow cooker.
Stir in the soup, milk, sour cream, Worcestershire sauce, garlic powder, chopped basil, cheese and black pepper until thoroughly combined. Cook the dip on LOW for 2-3 hours or until broccoli is tender and cheese is melted.
The dip may be set to the warm/low position until you serve it. Top with additional black pepper and fresh parsley. Best served warm with toasts.