In a large mixing bowl place 2 cups of the flour; set aside. In a small bowl combine the yeast, warm water, and 1/8 teaspoon sugar. Stir until yeast is dissolved; set aside. In a medium saucepan heat and stir the milk, butter, 1/3 cup sugar, and salt until warm (120 degrees F to 130 degrees F) and butter almost melts. Add to flour mixture along with the yeast mixture and eggs. Beat with an electric mixer on low to medium speed for 30 seconds, scraping sides of bowl constantly. Beat on high speed for 3 minutes. Stir in snipped apricots, raisins, and as much of the remaining flour as you can with a wooden spoon.
Turn dough out onto a lightly floured surface. Knead in enough remaining flour to make a moderately soft (not sticky) dough that is smooth and elastic (3 to 5 minutes total). Shape dough in a ball. Place dough in a lightly greased bowl, turning once to grease surface of dough. Cover and let rise in a warm place until double in size (about 1-1/2 hours).
Punch dough down. Turn out onto a floured surface. Cover and let rest 10 minutes. Grease two baking sheets; set aside. Divide dough into 20 portions; shape each into a smooth ball. Place balls 2 inches apart on prepared baking sheets. Cover; let rise until nearly double (45 to 60 minutes).
Preheat oven to 375 degrees F. Make a crisscross slash across top of each bun with a sharp knife or scissors. In a small cup combine beaten egg white and water. Brush mixture over buns. Bake for 12 to 15 minutes or until golden brown, rotating baking sheets halfway through baking. Top with apricot strips. Serve warm. Store remaining buns in an airtight container in the refrigerator up to 3 days. To reheat, place 1 or 2 buns at a time on a microwave-safe plate and heat 15 to 20 seconds. Makes 20 buns.