In a mixing bowl, blend softened cream cheese and buffalo wing sauce until smooth and creamy. Stir in the ranch or blue cheese dressing, followed by the shredded chicken, cheddar cheese, and optional chopped green onions. Cover the bowl and chill the filling in the refrigerator for 30 minutes.

Lay an egg roll wrapper on a clean, flat surface in a diamond shape. Place 2-3 tablespoons of the chilled buffalo chicken dip filling in the center of the wrapper. Fold the bottom corner up over the filling, then fold in the sides, before rolling tightly to form a sealed egg roll. Use a little egg wash to secure the top corner.

In a heavy-bottomed pot, pour enough vegetable or canola oil to cover the egg rolls while frying, typically around 2-3 inches deep. Heat the oil to 350-375°F (175-190°C) using a thermometer for accuracy.

Carefully drop 3-4 assembled egg rolls into the hot oil, ensuring not to overcrowd the pot. Fry them for 3-5 minutes, turning occasionally, until they are golden brown and crispy.

Once fried to a perfect golden brown, use a slotted spoon to remove the crispy buffalo chicken dip egg rolls from the oil. Transfer them to a plate lined with paper towels to absorb excess oil.

Allow the egg rolls to cool slightly before serving. Pair with ranch or blue cheese dressing for dipping.