Heat a large skillet over medium heat. Add the Italian sausage and diced onion, breaking the sausage into small crumbles as it cooks. Continue for 6–7 minutes, until the sausage is browned and fully cooked and the onion is tender. Drain any excess grease.
Reduce the heat to medium-low. Add the cubed processed cheese and cream cheese to the skillet. Stir frequently until both cheeses melt together into a smooth, creamy mixture.
Slowly whisk in the milk, followed by the dry mustard, Worcestershire sauce, smoked paprika, and black pepper. Continue stirring until the dip is hot, smooth, and easily scoopable.
Remove the skillet from the heat and immediately stir in the shredded sharp cheddar. Mix until the cheddar melts completely into the sauce. Adding it off the heat helps keep the dip smooth. Spend With Pennies
If the dip seems too thick, stir in an additional tablespoon or two of milk until it reaches your preferred dipping consistency. For a thicker dip, allow it to sit for a minute or two before serving.
If serving at a party, transfer the dip to a small slow cooker and keep it on the warm setting. Stir occasionally to maintain a smooth texture.
Sprinkle with chopped green onions and serve immediately with tortilla chips, crackers, crostini, pretzels, or sliced vegetables.