Make the Dough
Add the warm water, yeast, sugar, and olive oil to a large bowl and mix to combine. Let the mixture sit for about 5 minutes, until the yeast becomes foamy and bubbly.
While the yeast activates, set up your Mini Kitchen.
Add the honey, salt, egg, and flour to the yeast mixture. Mix until a sticky dough forms, then turn the dough onto a lightly floured surface. Knead for about 2 minutes, just until all of the flour is incorporated. The dough should be soft and slightly sticky. If it feels too sticky to work with, add the reserved 1 tablespoon of flour a little at a time as you knead.
Immediately divide the dough into 12 equal pieces and cover them with a clean towel while you prepare the apple filling.
Make the Apple Filling
Add the diced apples, honey or sugar, cinnamon, and water to a small pan. Cook over medium heat for about 5 minutes, stirring occasionally, until the apples have softened and the mixture is fragrant. Set aside to cool slightly.
Fill the Buns
Take one piece of dough at a time and roll or flatten it into a small circle. Place a spoonful of the apple filling in the center, then bring the edges of the dough up around the filling and pinch them together to seal. Gently roll it between your hands to form a smooth ball.
Place the filled buns into the Mini Kitchen, leaving a little space between them.
Close the Mini Kitchen, but do not turn it on yet. Let the buns rest inside for 10 minutes.
Open the Mini Kitchen and brush the tops of the buns lightly with beaten egg.
Mix the granulated sugar and cinnamon together, then sprinkle the cinnamon sugar over the tops of the buns.
Preheat the Mini Kitchen to 180–190°C. Once hot, bake the buns for 8–10 minutes, until they are golden brown and the tops are caramelized.
Turn off the Mini Kitchen and let them cool for a few minutes.
Make the Glaze
Whisk together the confectioners’ sugar, cinnamon, and honey. Add the water a little at a time, whisking until you have a thick but spreadable glaze. You want it smooth enough to spread over the tops of the buns without being runny.
Spread the cinnamon glaze over the slightly cooled buns and serve warm.