Prepare Basic Sweet Dough as directed through first rising.
While dough is rising, combine dates and water in a small saucepan. Cook over medium heat, stirring frequently, until most of the water is absorbed, about 2 minutes. Remove from heat. Stir in nuts. Cool.
Punch down dough. Roll out dough on lightly floured surface into a 15X9-inch rectangle. Spread butter over dough. Spread date mixture over butter. Roll up dough jelly-roll fashion, starting on 15-inch side. Pinch seam to seal. Arrange in circle on large greased cookie sheet. Pinch ends of dough together to seal. With scissors, cut 2/3 of the way through ring at 1-inch intervals, leaving center of the ring intact. Gently lay each section on its side, cut side up, to show date filling.
Brush with oil. Cover loosely with plastic wrap and let stand in warm place (85°F) until doubled, about 1 hour.
Heat oven to 350°F. Prepare Sugar Icing. Uncover dough and bake until evenly browned, 45 to 50 minutes. Remove from cookie sheet to wire rack. Spread with Sugar Icing. Cool.