1Tbspsugar(you can reduce if you like; if you prefer a more savory taste, you can increase the amount of soy sauce but you will need to add some sugar to balance out the salty flavor and can't omit it completely)
Using the fine mesh strainer, sift the flour into a large bowl. Combine hot water, oil, and kosher salt.
Mix the dry ingredients and wet ingredients with chopsticks until you can pick up the dough with hands.
Use the dough to pick up crumbs in the bowl.
Knead on a lightly floured surface for about 3 minutes, until a smooth dough forms. In Japan, we say “knead until the texture is like your earlobe”.
Form the dough into a ball, put it back in the bowl, cover with plastic wrap, and let it rest at room temperature for at least 30 minutes or longer. Letting the dough rest increases its elasticity making it easier to work with later, so please don't skip.
To Make Eggplant Filling
While the dough rests, make the fillings. Remove the eggplant stem and cut it half vertically. Then slice into half circles. Soak in water for 5-10 minutes (Meanwhile, you can cut Kabocha). Drain well and set aside.
Heat sesame oil in a large frying pan and sauté eggplant until it is coated with oil. Cover the lid and cook on low heat for 5 minutes.
When tender, add sugar and combine well.
Add miso and julienned shiso leaves, and mix well together. Transfer to a dish to let cool.
Cut each wedge into thin slices and then cut into thin strips.
Heat the oil in the frying pan and sauté the kabocha. When it’s coated with oil, add water and cook covered for 5 minutes on low heat.
Add sugar and combine well.
Add soy sauce and pinch of salt. Mix well together.
Transfer to the dish to let cool.
To Shape into Oyaki
Roll out the rested dough into a rectangular or circle shape and divide it into 12 pieces.
Make each dough into a ball then press down with your hand.
Stretch the dough to 10 cm (4 inches) in diameter. The important trick is to keep the center thicker than the edges. Using your fingers, stretch the outer edges by rotating the dough. This way, when you pinch the dough to seal, the dough won’t be too thick/too much.
Place about 1 Tbsp of the filling in the center of each piece of dough. Close the oyaki by bringing the dough up over the filling, pinching at the top to seal.
After pinching the dough, put the pinched-side down on a lightly floured surface and twist a few times. Then press the top of the oyaki a little bit into a slightly flat ball.
To Cook Oyaki
Set a steamer ready, by placing a steamer basket on top of wok/pot filled with enough boiling water. If you don’t have a steamer, after cooking the oyaki in a frying pan, add ¼ cup water to the pan. Cover with a lid and steam it until the water evaporates.
Heat the oil in a frying pan (12 inch) and cook oyaki, pinched-side down.
Pan fry for 3-4 minutes each side, or until golden brown.
Transfer the oyaki to a steamer basket and cover to cook on high heat for 15-20 minutes (depending on the size of the oyaki and filling – small one should take about 10 minutes). Make sure the lid is covered with the kitchen towel so condensation on the lid doesn’t fall onto the oyaki.
When they are done steaming, transfer to a wire rack (I use a bamboo strainer) where the heat can escape from the bottom.
To Serve and Store
Enjoy them immediately. As soon as they become warm, not hot, cover the leftovers with plastic wrap (I wrap individually). Don’t wait until completely cooled down. You can freeze to store for up to a month, and re-steam to enjoy later.