In the bowl of as stand mixer, add the warm milk, the yeast, sugar, salt, butter and eggs. Mix briefly to combine.
Add 5 1/2 cups of flour and using either a dough hook or paddle attachment, mix on low speed until flour starts to incorporate into the dough. Increase speed to medium. Add the remaining 1/2 cup flour slowly until dough pulls away from side of the bowl.
The dough should be soft and a little bit sticky. If it is too sticky to handle, add a little more flour at at time until you reach the desired consistency.
Transfer dough to a lightly oiled bowl, cover with a kitchen towel and allow to rise in a warm place for 90 minutes. It should double in size.
Lightly grease a baking sheet and form the rested dough into 24 even sized balls. Place on the baking sheet in 6 rows of 4. It's ok if they touch a little. Cover with a towel and allow to rise for another 1 hour.
Preheat the oven to 190 C (375 F), and bake the bread after it's second resting time for 12-14 minutes until golden brown.
As soon as it's out of the oven, brush the bread with the melted butter.