Combine flour, sugar, yeast, warm milk, 2 eggs, softened butter, and salt in a stand mixer bowl and knead with dough hook for 8 to 10 minutes until smooth and elastic.
Cover the dough and let rise in a warm place for 60 to 90 minutes until doubled in size.
Divide the dough into 8 equal pieces, shape each into a smooth ball, place on a parchment-lined baking sheet, cover, and let rise for 30 minutes until puffy.
Preheat the oven to 375°F / 190°C, brush the buns with the remaining beaten egg, and sprinkle with sesame seeds.
Bake for 16 to 18 minutes until golden brown and the internal temperature reaches 190°F / 88°C.
Cool on a wire rack for 10 minutes before slicing horizontally for burgers.