Make the dough. Pour the water into a small heat-proof bowl and microwave on high for 20 seconds, or until it reaches 110-115°F. Stir in the yeast and 1 tablespoon of the sugar, then cover with plastic wrap and let it bloom for 10 minutes, until it's foamy and frothy.
While the yeast is blooming, whisk together the flour, the remaining 2 tablespoons of granulated sugar, and the salt in the bowl of a stand mixer (or a large bowl).
Add the yeast mixture, the melted butter, and the egg. Using the dough hook attachment (or your hands), knead the dough on medium speed for 8-10 minutes, until it forms a smooth, slightly tacky but not sticky dough ball. If the dough is still too sticky, add more bread flour 1 tablespoon at a time.
1st rise. Transfer the dough to a greased bowl, cover with plastic wrap or a kitchen towel, and let it rest in a warm place until it doubles in size, about 1½ to 2 hours.
Shape the dough.(Step-by-step photos are in the blog post above.) Line a large baking sheet with parchment paper and set it aside. Punch down the dough and transfer it to a floured surface. Divide the dough into 6 equal portions and roll each into a ball.
Set a dough ball on the work surface. Rest the pinky side of your hand across it, about a third of the way in from one edge, and roll back and forth to squeeze that section thinner. You'll end up with a small ball on top of a bigger ball, joined by a short neck, like a snowman.
Press the whole thing flat with your palm, keeping the snowman shape. The bottom should be about 5 inches across and the top a little smaller.
Pick up the small end, twist it a half turn so it flips over, and lay it down on top of the bigger end. Press the whole bun flat again to about 5½ to 6 inches, pinching the edges so the seams seal. You'll see a curved ridge across the top where the two pieces meet. Repeat with the rest.
2nd rise. Transfer the shaped buns onto the prepared baking sheet. Cover with plastic wrap or a kitchen towel and allow them to rise in a warm place until almost doubled in size, about 1 to 1½ hours. During the last 20 minutes of rising, preheat the oven to 350°F.
Bake. Make the egg wash by whisking together the egg yolk and 2 teaspoons of water until combined. Brush the egg wash over the tops of the buns, then sprinkle generously with sesame seeds.
Bake for 25-30 minutes until golden brown. Let the buns sit on the baking sheet until they're easy to handle, then move them to a wire rack and let them cool completely. Slice and serve as a sandwich or add your favorite fillings.
Notes
Storing and freezing. Keep cooled buns in a zip-top bag or airtight container at room temperature for up to 4 days. To freeze, wrap each bun tightly and store in a freezer bag for up to 3 months, then thaw at room temperature.
Yeast. Active dry yeast works in place of instant; it just takes longer to rise. Bloom it the same way and plan on extra time for both rises.
Flour. All-purpose flour works if that's what you have, but the buns will be softer and a little less sturdy for a big sandwich.
Loose seams. If the seams aren't fully sealed, the top may pull apart in the oven and bake up lopsided.
Slicing. Slicing while warm makes the inside dense and gummy, so wait until they're completely cool.