Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper or lightly grease it.
In a medium bowl, combine cream cheese, green onions, garlic, Worcestershire sauce, soy sauce, black pepper, and parsley if using. Mix until smooth and well combined.
Place one egg roll wrapper on a clean surface in a diamond shape. Add 1–2 tablespoons of filling near the bottom corner. Fold the bottom over the filling, then fold in the sides and roll up tightly. Seal the edge with a bit of water. Repeat with remaining wrappers and filling.
Place the rolls seam-side down on the prepared baking sheet. Lightly spray or brush the tops with olive oil or melted butter. Bake for 18–20 minutes, flipping halfway through, until golden and crisp.
Remove from the oven and let cool slightly. Serve warm with dipping sauce of your choice.