For the steamed bun dough: In a small bowl, swirl together the water, yeast and 1 teaspoon of the sugar and let it sit until it becomes foamy on top, about 5 minutes.
In a large bowl, mix together the all-purpose flour, cake flour, salt and remaining 6 tablespoons sugar. Pour in the yeast mixture and oil and mix to form a dough. Turn out onto a work surface and knead, dusting with flour as needed, until the dough is smooth and slightly sticky, about 5 minutes. Transfer the dough to an oiled bowl, turning to coat, cover the bowl with plastic wrap or a damp towel and let it rise until doubled in size, about 2 hours.
For the filling: While the dough is rising, preheat the oven to 425 degrees F.
Place the carrots in a baking dish and toss with the oil and salt. (I like baking them in a high-sided dish like a casserole, so that I have room to add the other filling ingredients and then there's no need to transfer to a bowl.) Bake until tender, 30 to 35 minutes; let cool for 5 minutes.
Add the teriyaki sauce, peanuts, rice vinegar, scallions and a drizzle of sriracha to the carrots and stir together. Set aside to continue to cool. It's ok if it's still a little warm when it's time to fill the buns. The filling can be made a day in advance and kept covered in the fridge.
Once the dough has completed its rising time, turn it out onto a clean work surface and divide it into 16 balls. Keep the dough balls covered when you're not working with them. Working with 1 ball at a time, roll out to a 4 1/2- to 5-inch circle, fill with about 2 heaping tablespoons of filling and pinch the edges shut to seal well. Place on an individual 3-inch square of parchment paper. Space the buns out in a steamer basket 1 1/2 to 2 inches apart. (If your steamer doesn't fit all of the buns at once, do in batches.) Cover and let rise 30 more minutes.
Bring a large pot of water to a boil over high heat (the water should come up high in the pot so it is close to the steamer). Place the steamer over it and steam the buns until light and fluffy, about 45 minutes.
To serve, top with another little drizzle of sriracha and some sprinkles of peanuts and scallions. Dip in teriyaki sauce and enjoy!
Leftovers can be cooled and kept in the fridge for a couple of days or in the freezer for a few months. To reheat, wrap them in a damp paper towel and microwave until heated through.