Place the frozen loaves on a tray and thaw at room temperature for 3 to 4 hours, or thaw them in the refrigerator overnight.
Spray three 9-inch bread pans with nonstick cooking spray and set them aside.
Cut four deep cuts into each loaf, nearly all the way through while leaving a small piece connected at the bottom.
Coat each loaf completely with melted butter, working the butter well into every cut.
Mix the granulated sugar and cinnamon in a wide dish. Roll each loaf gently in the cinnamon sugar, making a thick coating and filling the cuts generously.
Place one loaf in each pan, cover loosely with a light tea towel, and let the dough rise in a warm area until doubled, about 1 hour.
Preheat the oven to 350°F.
Bake for 20 to 25 minutes, until golden brown and hollow-sounding when tapped on the bottom. Cool for about 10 minutes.
Whisk the powdered sugar, vanilla, and 2 tablespoons of milk for the icing, adding more milk as needed. Drizzle it over the warm bread and serve.