Make baked sweet potatoes: Wash 17.6 ounces Japanese sweet potatoes and wrap them tightly with aluminum foil. Place them in a non-preheated oven and bake at 320°F (160°C) for 90 minutes. Turn off the oven and let them sit for 10 minutes (see Note 2). If using leftover baked Japanese sweet potatoes, reheat them at this time.
Prepare the egg yolk mixture: Remove 1 teaspoon per batch from 1 egg yolk and mix it with ½ teaspoon water. Set aside for brushing later.
Mash the sweet potatoes: While still hot, peel the sweet potatoes and transfer about 1½ cups (400g) of the flesh per batch to a medium pot. Mash until smooth.
Mix the ingredients: Add 2 tablespoons unsalted butter and mix well until fully melted. Add the remaining egg yolk and ¼ teaspoon kosher salt, then knead with a spatula until smooth. Add sugar if you prefer a sweeter taste.
Adjust the consistency: Scoop up the mixture with a spatula—it should be creamy enough to slowly drop off the spatula due to gravity but firm enough to hold its shape on the spatula. If too firm, add ~1 tablespoon milk little by little until the right consistency is reached.
Heat and knead: Heat the pot over low-medium heat, stirring and kneading with a spatula. Continue until the surface becomes shiny and stops sticking to the spatula. Let it cool until comfortable to touch.
Preheat the oven: Preheat the oven to 430°F (220°C) and move the oven rack to the second-highest position.
Prepare the baking sheet: Place aluminum cups on a baking sheet and brush with melted butter or oil. Or, use baking paper instead of aluminum cups.
Shape the dough: Once cooled, divide the dough into serving-sized portions. Shape each into a rugby ball and place them in aluminum cups or on the baking sheet.
Bake the dessert: Brush each piece with the egg yolk and water mixture, then bake for about 10 minutes or until the surface turns golden brown (see Note 3).
Cool and enjoy: Let them cool slightly before serving. Enjoy!