Combine ranch dressing with cream cheese and let sit for 10 - 15 minutes or longer so the flavors integrate.
Clean the mushrooms and remove the stems, leaving only the caps.
When the cheese has rested, use a teaspoon to fill the mushroom caps with the herb cheese mixture.
Combine the flour with 1 1/2 teaspoons salt and cayenne pepper in a small bowl.
Pour the milk into another bowl.
Dip each mushroom first into the milk, then into the flour. Do this twice for each mushroom so that each has been double-coated.
Put the coated mushrooms into the freezer for at least 3 hours. This will keep the coating from falling off, and it will keep the cheese inside from expanding too fast and leaking out of the mushroom when frying.
Meanwhile, make the dipping sauce by combining all of the ingredients ina small bowl. Keep the sauce covered and chilled until ready to serve it.
When the mushrooms are frozen, heat the oil in a deep fryer or deep pot to 350 degrees F.
Use enough oil to completely cover the mushrooms (or at least a couple of inches deep). Fry the mushrooms for 8 - 10 minutes or until the outside turns a golden brown. Drain the mushrooms on a rack or paper towels.
Let the mushrooms sit for a couple of minutes before serving- they will be very hot on the inside. Serve with the dipping sauce on the side.