In a bowl, dissolve 1 tablespoon of sugar and ¾ teaspoon of instant yeast into 180 grams of water. Stir until fully incorporated.

Gradually pour the mixture into 350 grams of all-purpose flour while stirring simultaneously. Once the mixture starts to form a rough dough, use your hands to gather the flour and knead gently. Add 2 teaspoons of vegetable oil and knead further until the dough becomes smooth and pliable. This step ensures the buns remain soft and fluffy even after cooling, as the oil prevents the starch from retrogradation. Cover the dough and let it proof for 1.5 hours or until it has doubled in size.

While the dough is proofing, prepare the filling. Blend the roasted peanuts and sesame seeds coarsely. In a mixing bowl, combine them with 140 grams of white sugar and 4 teaspoons of all-purpose flour. Mix thoroughly. The sugar will melt during steaming, and the flour will act as a stabilizer, preventing the filling from leaking out.

Once the dough has doubled in size, punch it down to release air bubbles. Knead it for about 6 minutes until it regains a smooth texture. Divide the dough into 10 equal portions, each weighing approximately 50-55 grams. Cover the portions with plastic wrap and let them rest for 10 minutes. This resting period helps to relax the gluten, making it easier to roll out.

Dust one dough ball with a small amount of flour to prevent sticking. Using a rolling pin, flatten it into a disc about 4 inches in diameter. Lift the disc and thin out the edges further while leaving the center slightly thicker. Roll the disc into a wrapper approximately 5 inches in diameter.

Place the wrapper on your hand and curve it to form a small bowl shape. Spoon 2 tablespoons of the sugar-nut filling into the center. Fold pleats around the edge to seal the bun, ensuring the filling is enclosed. Repeat this process with the remaining dough and filling.

Arrange the filled buns in a steamer, leaving space between each bun to allow for expansion. Use parchment paper underneath each bun to prevent sticking. Cover the steamer and let the buns proof for another 30 minutes.

Fill a pot with room-temperature water and place the steamer on top. Turn the heat to high. When steam starts escaping from the steamer, reduce the heat to medium-low. Steam the buns for 10 minutes.

After steaming, turn off the heat but do not open the steamer lid immediately. Allow the buns to rest inside the steamer for at least 5 minutes. This prevents the buns' skin from shrinking when exposed to cold air, preserving their fluffiness.

Enjoy the freshly steamed bao buns warm, with their tender wrappers and sweet nutty filling.