Depending on how much liquid you add, it can be as thick or thin as you like. Make a thick dip for crackers and veggies, or thin it out to be more spreadable to use as a condiment on burgers or sandwiches.
Mix together all ingredients, except milk, using an electric mixer. Slowly pour in milk until you get the thickness you want.
For a dairy free option, use a soft tofu in place of the cream cheese and omit the Parmesan and milk. Adjust the other ingredients to taste, and add more tofu if needed until you get the consistency you desire.