In a small bowl, sprinkle the yeast over the water and stir to dissolve. Set aside.
Add the flour, sugar, 2 teaspoons of rosemary, and salt to the bowl of a stand mixer. Whisk to combine.
Add the milk, egg, and yeast mixture. With the dough hook on medium speed, knead the dough until combined. Slowly add the oil and continue kneading until the dough becomes soft, pulls away from the sides of the bowl, and is no longer sticky.
Form a smooth ball with the dough and let sit in the bowl, loosely covered, in a dark and warm place. Let rise for about 1 hour, until doubled in size.
Divide the dough into 12 even pieces. Roll each ball into a 15-inch long rope. Coil each rope by rolling it upon itself, from left to right. Lay onto a greased or lined baking sheet, leaving about 2-inches between each roll. Cover and let rise in a dark and warm place for about 30 minutes, until doubled in size.
Preheat oven to 350°F.
Whisk the egg and milk together in a small bowl. Brush over the risen rolls and sprinkle on the remaining 1 teaspoon of rosemary. Bake for 18 to 20 minutes, until golden brown. Transfer to a cooling rack until warm to the touch.