Preheat the oven to 350 degrees F. Stir together the butter and brown sugar in a medium bowl until smooth. Stir in the maple syrup, vanilla and salt. Stir together the granulated sugar and cinnamon in a small bowl.
Cut the bread lengthwise into 1/2-inch slices without cutting through the bottom of the crust. Then cut the bread crosswise into 1/2-inch slices without cutting through the bottom of the crust. Spoon and push the butter mixture into all of the cuts in the bread. (You may have extra butter mixture, it will just depend on how large your loaf is.) Sprinkle about 1/2 cup of the cinnamon sugar in the cuts and over the top.
Wrap the loaf in foil, place on a baking sheet, and bake until hot and all the butter is melted, 25 to 30 minutes. Open the foil, sprinkle over the remaining cinnamon sugar and bake until the crust is lightly golden brown and crispy, about 10 minutes longer. Transfer to a cutting board or platter and let cool for 10 minutes.
Put the confectioners' sugar in a small bowl and slowly stir in the milk until you have a thick but pourable icing. Drizzle the icing over bread and serve immediately.