Combine the yeast and warm water and set aside for 10 minutes.
Warm 3/4 cup of the milk in the microwave. In a large bowl, combine 4 tablespoons of the melted butter and the warm milk. Using an electric mixer with a dough hook at low speed, or a wooden spoon, slowly stir the dissolved yeast into the butter and milk. Add 1/2 cup of the granulated sugar, the egg and the salt, and mix until combined. Add 4 cups of the flour, 1/2 cup at a time; mix until smooth. If the dough is sticky, add up to 1/2 cup of flour.
Knead the dough on a floured surface for 5 minutes, place in a medium bowl and cover with plastic wrap. Let rise until doubled in size, about 1 hour.
Stir together the brown sugar, the remaining 1/4 cup of granulated sugar and the cinnamon. On a floured surface, roll out the dough to form a 12-by-24-inch rectangle. Brush the remaining 3 tablespoons of melted butter over the dough, and sprinkle the brown sugar mixture on top. Scatter the raisins over the dough.
Starting with a long side, roll the dough up into a log, jelly-roll style, then cut with dental floss or a sharp knife into generous 1-inch slices. Place in 3 greased 9-inch round cake pans (about 7 rolls per pan). Let the rolls rise for 45 minutes.
Preheat the oven to 350 degrees . Bake the rolls, uncovered, until crusty and golden on top, about 25 minutes.
Stir together the confectioners sugar, vanilla and the remaining 3 tablespoons of milk until smooth. Drizzle over the rolls and serve.