Warm the milk and water in a small saucepan until it bubbles, and then remove from heat. Mix in the butter until dissolved. Let cool until warm, not too hot.
In a large bowl, combine the bread mix, sugar and yeast, add eggs and warm milk mixture. Beat well until smooth. Cover and let rise in a warm place for 1 hour.
Dough will be sticky, add rice flour as needed to separate dough away from bowl. Turn the dough onto a well-floured work surface and knead slightly and form into a round ball.
Roll out to about 1/2 inch thick. Cut rounds with a 3-inch biscuit cutter or drinking glass.
Heat a large nonstick frying pan over a steady low heat to prevent burning.
Place each muffin about 2 inches apart. Cover with a lid and cook for about 5-6 minutes on the first side, flip over and cook on the other side for 4-5 minutes. The steam created from the lid will help the muffins rise and cook better.
*To use, split and toast. Great with cream cheese, jam or make a delicious breakfast sandwich.