Cook first 5 ingredients in a heavy saucepan over medium heat, stirring often for 2 minutes or just until it begins to steam. Remove from heat. Stir in butter until it melts. Cool completely.
Combine flour and next 3 ingredients in a large bowl; make a well in center of mixture.
Stir the egg into the milk mixture until well blended. Add to the flour mixture, stirring just until moistened.
Spoon 1/3 of batter into each cup of a lightly greased 12-cup muffin pan. Add 2 teaspoons of goat cheese to each cup. Spoon remaining batter evenly over goat cheese in each cup.
Bake for 20-25 minutes or until golden brown. Cool in pan on a wire rack for 5 minutes, then remove muffins from pan.