Preheat oven to 400F (200C).
Cut sweet potato into 1/2" (1.2 mm) thick rounds. Let soak in water for 10 minutes. Cook in boiling water until tender. Peel the skin and mash. Sieve through a mesh strainer if you want a smoother texture.
Mix mashed potato with sugar and soft butter. Add rum. Chill the potato mixture in the fridge for 30 minutes.
Mix yolk and Mirin to make egg wash.
Shape potato mixture into 12 oblong shapes. Place on a baking sheet lined with parchment paper, and brush the surface with the egg wash. Sprinkle with sesame seeds.
Bake in the preheated oven for 20 minutes or until browned.