Combine the milk, sugar, melted butter, salt, and yeast in the bowl of a stand mixer fitted with the hook attachment and stir to combine well. Add the eggs and stir until well mixed. Add the flour and mix on medium-high speed until the dough is smooth and elastic, about 4 minutes. Transfer the dough to a large, lightly oiled bowl and cover with plastic wrap or a clean kitchen towel. Let stand in a warm, draft-free place until doubled in size, 1 1/2 to 2 hours. Punch the dough down and lightly flour a work surface. Lay the dough out and roll the dough out into an 18-by-12-inch rectangle.

Butter a 13-by-9-inch glass baking dish. Spread the softened butter evenly all over the dough, leaving a 1/2-inch border, then sprinkle evenly with the brown sugar and cinnamon. Sprinkle raisins, if using. Roll up the dough and press and crimp the edges to seal. Cut the dough into 12 slices and arrange them in the buttered baking dish. If you want to bake them the same day, cover with plastic wrap and let stand until doubled in size, about 1 hour. Otherwise, refrigerate overnight; take out of the refrigerator and let sit at room temperature for 1 hour before baking. Preheat the oven to 375 degrees F. Bake the cinnamon buns until puffed and golden brown all over, about 25 minutes.

Put the icing sugar in a medium bowl. Whisk in the melted butter, vanilla and milk Whisk until smooth. Add additional milk, about 1 teaspoon at a time, if needed to achieve the right consistency. Drizzle the icing over the warm cinnamon rolls. Serve warm.