Combine yeast and warm water; let stand 5 minutes. Combine yeast mixture, 1/4 cup sugar, and salt. Add 2 cups flour, potato, and oil; beat at medium speed of an electric mixer until well blended. Stir in enough of the remaining 3 cups flour to make a soft dough.
Sprinkle 3 tablespoons flour over work surface. Turn dough out; knead until smooth and elastic (about 8 minutes). Place in a bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down; roll to a 24- x 6-inch rectangle. Brush with margarine. Combine 1/2 cup brown sugar and cinnamon; sprinkle over dough. Roll up, starting at long side. Pinch seam to seal (do not seal ends). Cut into 16 (1 1/2-inch) slices.
Spoon remaining 3/4 cup brown sugar into a 13- x 9- x 2-inch baking dish coated with cooking spray. Sprinkle currants and pecans over sugar. Place slices over sugar. Pour milk around rolls. Cover and let rise in a warm place, free from drafts, 30 minutes or until doubled in bulk. Bake at 375° for 30 minutes or until done. Let cool 2 minutes.