In a mixing bowl, dissolve yeast in warm milk. Add the butter, sugar, salt and egg yolk; mix well. Stir in enough flour to form a soft dough.Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour
Punch dough down. Shape into 12 balls. Push thumb through centers to form a 1-in. hole. Place on a floured surface. Cover and let rest for 10 minutes;
In a large saucepan, bring water to a boil. Drop bagels, one at a time, into boiling water. When bagels float to the surface, remove with a slotted spoon and place 2 in. apart on greased baking sheets. Bake at 400 degrees F for 20-25 minutes or until golden brown. Remove from pans to wire racks to cool.