In a large mixing bowl (or stand mixer bowl), combine warm milk, a pinch of sugar, and active dry yeast. Stir gently and let sit for 5-10 minutes until foamy, indicating the yeast is active.

To the foamy yeast mixture, add the remaining 2 tbsp granulated sugar, melted butter, and room temperature egg. Whisk until well combined.

In a separate bowl, whisk together 3 ½ cups of all-purpose flour and salt.

Gradually add the dry ingredients to the wet ingredients, mixing with a wooden spoon or a dough hook on a stand mixer on low speed. Once a shaggy dough forms, increase speed to medium-low and knead for 8-10 minutes until the dough is smooth, elastic, and pulls away from the sides of the bowl. If kneading by hand, turn the dough out onto a lightly floured surface and knead for 10-12 minutes. The dough should be slightly tacky but not sticky. Add more flour one tablespoon at a time if too sticky.

Lightly grease a clean large bowl with a little oil. Transfer the dough to the bowl, turning once to coat. Cover the bowl tightly with plastic wrap or a clean kitchen towel and let it rise in a warm, draft-free place for 60-90 minutes, or until doubled in size.

Gently punch down the risen dough to release air. Turn it out onto a lightly floured surface. Divide the dough into 8 equal pieces (approximately 90-100g each for standard buns). Roll each piece into a smooth, tight ball.

Line two baking sheets with parchment paper. Arrange the shaped dough balls on the prepared baking sheets, leaving about 2-3 inches between each bun. Lightly flatten each ball slightly with the palm of your hand to create a wider base. Cover loosely with plastic wrap or a clean kitchen towel and let rise again in a warm place for 30-45 minutes, or until noticeably puffy and almost doubled in size.

While the buns are proofing for the second time, preheat your oven to 375°F (190°C). In a small bowl, whisk together the remaining large egg and 1 tbsp water to create an egg wash.

Just before baking, gently brush the tops of the proofed buns with the egg wash. If desired, sprinkle with sesame seeds. Bake for 15-20 minutes, rotating the baking sheets halfway through, until the buns are golden brown on top and sound hollow when tapped on the bottom.

Transfer the baked buns to a wire rack to cool completely before slicing and serving. Enjoy your homemade Burger Buns!