Place bittersweet chocolate and semisweet chocolate baking chips in a glass bowl; set aside.

Combine heavy whipping cream, cinnamon, and cayenne pepper in a medium saucepan. Cook over medium0high heat until simmering. Pour hot cream mixture over chocolate. Let stand 30 seconds; then whisk until smooth.

Use an apple corer to cut and remove centers from muffins; reserve centers for garnish. Spoon chocolate mixture into each muffin. Top with a small piece of served muffin centers; sprinkle with coarse sugar. Before serving, heat each muffin in the microwave on high for 15 seconds.