Soften compressed yeast in potato liquid. Let stand 5 minutes. (Or substitute 2 packages dry yeast softened in very warm, not hot, liquid.) Combine mashed potatoes, 3 tablespoons melted butter, 1/4 cup sugar, 2 teaspoons salt*, vanilla, and unbeaten eggs in large bowl. Add the softened yeast. Gradually add flour to form a stiff dough. Cover with waxed paper or towel. Let rise in warm place (85° to 90°F.) until light and doubled in size, about 1 1/2 hours. Meanwhile prepare Honey Nut Topping.
Combine all topping ingredients except 1/2 cup chopped nuts in saucepan. Bring to boil and cook, stirring constantly, until a little syrup dropped in cold water forms a soft ball (234°F.), about 1 1/2 minutes. Pour into greased 13x9x2-inch pan.** Sprinkle with 1/2 cup chopped nuts.
Toss dough on well-floured board until coated with flour and no longer sticky. Roll out to 24x8-inch rectangle. Brush with 2 tablespoons melted butter. Sprinkle with 1/4 cup brown sugar and 1/4 cup chopped nuts. Roll as for jelly roll, starting with 24-inch side. Cut or "tie off" with strong thread into twelve 2-inch slices. (To tie off slices, place thread under roll and pull ends around, crossing as if to tie in knot.) Place cut-side down over topping. Cover. Let rise in warm place until light and doubled in size, 30 to 45 minutes.
Bake in moderate oven (375°F.) for 25 to 30 minutes. Cool 2 minutes, then invert on serving plate or on rack over waxed paper. Let stand 30 seconds before removing pan.