Dissolve yeast in 1/2 cup warm water. Combine egg, sugar and salt in large mixer bowl. Blend well with electric mixer. Add oil, milk, water and the dissolved yeast. Add flour, 1 cup at a time until soft dough forms. Knead on lightly floured surface for 5 to 6 minutes. Place in a greased bowl, turning to coat. Cover and let rise in a warm, draft-free place about 1 to 1-1/2 hours, until doubled.
Punch dough down; divide in half. Roll one portion of dough on a lightly floured surface to a 12 x 15-inch rectangle. Spread evenly with 1 can apricot pastry filling. Roll up tightly, sealing edges. Place dough on greased 15 x 18-inch cookie sheet. Form dough into a circle, sealing the ends that meet. Snip through the circle at 1-1/2 inch intervals with scissors, cutting 2/3 of the way through the dough, cutting from the top. Repeat with other portion of dough. Cover and let rise 30 to 45 minutes. Bake in preheated 350°F oven for 25 to 30 minutes. Cool for 15 minutes. Combine icing ingredients and drizzle over rolls. Garnish with apricot halves.
Variation: Use raspberry pastry filling in place of apricot. Garnish with pecan halves.