Pull apart seam in apricot, and peel 3/4 way open. Stuff a small piece (about 1/4-inch square) of each dark chocolate and Appenzeller inside the apricot, and reseal shut. Repeat for all 36 apricots.
In a skillet pan over medium-low heat, melt butter. Add stuffed apricots, and let cook for 2 to 3 minutes. Flip. Cook an additional 2 to 3 minutes, or until chocolate and cheese are melted. Remove from pan. Place on serving platter, and sprinkle with black pepper.