In a large bowl, combine the warm milk, yeast, and sugar. Mix to combine then set aside to bloom 5-10 minutes.
Whisk in the salt and egg. Add 2 cups flour and mix until a shaggy dough. Add in the cubed, softened butter, and mix until the butter is incorporated.
Turn out the dough on a floured surface, adding 1/2 cup more flour at a time. Knead an additional 1-2 minutes, until a smooth and pliable dough.
Place in a greased bowl, then set aside in a warm environment for 30-45 minutes to double in volume.
Roll out the dough to be 1/4" thick rectangle. Slice into 4 strips lengthwise. Stack two strips on top of each other, so you know have two double-layered strips. Roll out each strip so it's 1/2" thick. Slice into 2" wide mini rolls. Pinch on end together so that it will open like a pocketbook. Place in a buttered 9x13" baking dish. Cover and set aside to rise 20-30 minutes.
Preheat the oven to 375F.
Brush the rolls with butter or an egg wash. Bake 12-15 minutes, until golden on top. Be careful not to over bake the rolls or they will be tough.
Mix the melted butter and honey together, then brush on top of the warm rolls. Set aside until ready to be used.