In a mixing bowl, let yeast and water stand for 5 minutes. Add sugar, milk, oil, salt, eggs and 2 cups flour; beat on low 3 minutes. Stir in enough remaining flour to form a soft dough. Turn onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl; turn once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Combine first five filling ingredients in a saucepan. Cook and stir over medium heat until thickened, 7-8 minutes. Stir in preserves; let cool.
Punch dough down; divide into thirds. On a floured surface, roll each portion into a 15-in. x 6-in. rectangle. Place on greased baking sheets. Spread a third of filling down the center third of rectangles. On each long side, cut 1-1/2-in. wide strips 1-3/4 in into center. Starting at one end, fold alternating strips at an angle across filling. Cover and let rise for 30 minutes or until doubled. Bake at 375 degrees F for 15-20 minutes or until browned. Cool on wire racks. Combine icing ingredients; drizzle over braids.