In a large bowl, combine the flour, sugar, yeast, salt and nutmeg. In a small saucepan, heat the milk, water and butter to 120°-130°. Add to dry ingredients; beat until moistened. Beat in eggs until smooth. Cover and refrigerate overnight.
In a large saucepan, combine apricots and water. Cook over medium heat for 30 minutes or until the water is absorbed and apricots are tender. Remove from the heat; stir in the brown sugar, juice and nuts. Cool.
Punch dough down. Turn onto a lightly floured surface; divide in half. Roll one portion into an 18-in. x 12-in. rectangle. Spread half of filling over rectangle to within 1/2 in. of edges. Roll up jelly-roll style, starting with a long side; pinch seam to seal.
Place seam side down on a greased baking sheet; pinch ends together to form a ring. Repeat for second ring. With scissors, cut each from outside edge two-thirds toward center of ring at 1 in. intervals. Separate strips slightly: twist so filling shows, slightly overlapping with previous piece. Cover; let rise in a warm place until doubled, about 1 hour.
Bake at 375° for 25-28 minutes or until golden brown. Remove from pans to wire racks to cool.
In a small bowl, combine confectioner's sugar and enough milk to achieve desired consistency; drizzle over warm tea rings. Yield: 2 rings (12 slices each).