Clean mushrooms and remove stems. When cheese has rested, use a teaspoon to fill mushroom caps.
Combine flour, 1 1/2 teaspoons salt and cayenne pepper in a small bowl.
Pour milk into another small bowl. Dip mushroom first in milk and then in flour. Do this twice. Put coated mushroom into the freezer for at least 3 hours. When mushrooms are frozen, heat oil in a deep fryer to 350 degrees F. Use enough oil to cover mushrooms completely. Fry for 8 to 10 minutes until golden. Drain. Let sit for a couple of minutes before serving.