Grease a 10" square pan or 9" x 13" pan.
In a medium box combine the apple juice with the raisins, cover with plastic wrap or a glass lid and microwave just until warm, about 30-60 seconds, and the plastic begins to shrink around the bowl. Set aside to cool to room temperature.
After it's cool, mix together all of the dough ingredients except the raisins, and knead, using an electric mixer or bread machine, Knead until the dough is soft and elastic. Mix in the raisins and apple juice mixture.
Cover with a towel or plastic wrap and let the dough rise for about 1 hour. It should become puffy but it may not double in size.
Divide the dough into similar sized pieces, about 3 3/4 ounces each. A heaped muffin scoop (about 1/3 cup) makes about the right portion. This makes about 12 to 14 buns. Using greased hands shape them into round balls. Place in the greased pan.
Cover the pan, and let the buns rise for 1 hour, or until puffy and touching one another. Meanwhile, preheat the oven to 375°F.
Whisk together the reserved egg white and milk. Brush over the buns.
Bake for 20 minutes and golden brown. Remove and place on a rack to cool.