1.In a medium bowl, add 1 cup flour, yeast, sugar and salt. In a small bowl, combine the water and butter. Heat in microwave until warmed. To the water-butter, stir in the egg yolk and 1/2 teaspoon vanilla. Immediately pour this mixture over the flour mixture in the bowl. (Don't let it set or the hot water will cook the egg yolk).
2.Stir the dough together and then spread it in a greased 9x5" loaf pan. It's okay if it doesn't touch the edges of the pan.
3.Cover the dough, and let it rise in a warm place until it doubles in size, about 45 minutes.
4.Preheat the oven to 350. In a medium bowl combine 3 tablespoons flour, 3 tablespoons sugar, light brown sugar, and cinnamon. Then work in the butter into the dough with your fingertips. Spread it over the dough.
5.Bake the coffee cake for 30 minutes, testing with a toothpick for moist crumbs before removing it from the oven.
6.While the cake cools slightly, whisk together powdered sugar, milk, 1/4 teaspoon vanilla. Drizzle over the cake and serve.