Preheat oven to 425F. Line a baking pan with parchment paper.
In the bowl of a stand mixer fitted with the hook attachment, combine the 2 tablespoons warm water, honey, and active dry yeast. Mix well then let bloom for 5 minutes, until foamy.
Add the remaining 1 cup warm water, olive oil, beaten egg, and salt. Mix to combine.
Add 3 cups of the flour to knead on LOW speed for 3-4 minutes, until most of the flour is absorbed. Add the additional ½ cup flour if the dough is too sticky. Knead until a smooth and pliable dough, about 3-4 minutes.
On a clean surface, divide the dough into 8 equal sized balls. Roll in the palms of your hands for a smooth ball.
Evenly distribute between on the baking pan and wet your fingers to press down on each burger bun ball to flatten to ½” thick.
Let rise 10-15 minutes.
Brush with an egg wash, then sprinkle with sesame seeds.
Bake for 8-12 minutes, until deeply golden on top, rotating the pan halfway through baking.
Let cool at least 20 minutes before using. Enjoy!