Whisk milk with egg and vanilla. Add milk mixture, flour, sugar, salt, butter, and yeast, in the order suggested by your bread machine manufacturer.
Set on dough cycle and add the blueberries and cinnamon at the beep for adding ingredients. If the dough seems very sticky (or very dry) at this point, add a bit of flour (or water) in very small amounts.
On floured surface, punch the dough down. Break off pieces of dough and shape into balls. Place side-by side in the prepared pan. Cover and let rise for 45 minutes. Heat oven to 350. Beat the egg yolk with 2 tablespoons of water and brush lightly over the tops of the huns. Bake the blueberry buns for 20-25 minutes, until nicely browned.
For Icing: Put powdered sugar in a small bowl. In a microwave-proof cup or small bowl combine butter with water and vanilla. Microwave until butter is melted and mixture is very hot. Pour into the powdered sugar and mix until well blended and smooth. Add very small amounts of hot water until you get a good drizzling consistency. You can put the mixture in a squeeze bottle and warm again in the microwave before drizzling over the buns; you can also drizzle with a spoon.
NOTE: Blueberries may be exchanged in this recipe for any other dried fruit, such as...cranberries, craisins, cherries..etc.