1. In a small saucepan, heat milk and the 1/3 cup (75 ml) butter over medium heat until butter is melted. Let cool to around 100°F (38°C).

2. In the mixer bowl, stir together yeast, water and a pinch of sugar. Let stand until yeast begins to foam, about 5 minutes. Add milk mixture, sugar, salt and eggs. Attach the flat beater and mixer bowl to the mixer. Set to speed 2 and mix until combined. Add 4 cups (1 L) of the flour and mix until a dough forms.

3. Remove the flat beater and attach the dough hook. Set to speed 2 and knead, adding flour ½ cup (125 ml) at a time, until dough forms a smooth and elastic ball that cleans the bowl. Continue to knead for 2 minutes, adding flour 1 tbsp (15 ml) at a time as necessary to keep dough from clinging to the bowl. (You may not need all of the flour. Save the remainder for dusting.) Using your hands, form dough into a ball. Place back in the mixer bowl, rub with softened butter and cover loosely with plastic wrap. Let rise in a warm, draft-free place for 1 to 2 hours, or until doubled in bulk.

4. Uncover dough and punch down several times to work out air bubbles. Turn over in the bowl. Cover with plastic wrap and let rise until doubled in bulk, about 1 hour.

5. Uncover dough and punch down again. Turn dough out onto a lightly floured work surface and cut into 12 equal pieces. As you work with each piece of dough, keep the rest covered. Working with one piece at a time, shape dough into a smooth ball. Flatten slightly with the palm of your hand and place on prepared baking sheet. If desired, brush tops with egg wash and sprinkle with sesame seeds. Repeat with remaining dough, placing at least 4 inches (10 cm) apart on sheets. Cover with towels and let rise for 30 minutes, until slightly risen. Flatten gently again. Meanwhile, place oven racks in the lower middle and upper middle positions and preheat oven to 375° (190°C).

6. Bake for 25 to 30 minutes, switching baking sheets halfway through, until buns are golden and reach an internal temperature of 200°F (100°C). Remove to wire racks and let cool completely.