Combine flour, sugar, yeast, warm milk, 2 whole eggs plus 1 egg white, softened butter, and salt in a stand mixer with dough hook and knead on medium speed 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 spaced 3 inches apart, cover, and let rise for 30 minutes until puffy.
Preheat the oven to 375°F / 190°C, brush the buns with egg yolk mixed with 1 tablespoon water, and sprinkle with sesame seeds.
Bake for 16 to 18 minutes until deep golden brown and the internal temperature reaches 190°F / 88°C.
Cool on a wire rack for 10 minutes, then slice horizontally and use for burgers or sliders.