In small saucepan over medium heat, in hot oil, cook onion, covered, until tender but not brown. Stir in roast beef spread, tomato sauce, pepper sauce, garlic and oregano; simmer 5 minutes. Spoon filling into bowl; cool.
Meanwhile, cook potato and peel off skin. Coarsely chop potato pulp. Stir potato pieces, olives and chopped egg into filling.
Preheat oven to 400 degrees. Line large baking sheet with nonstick foil.
On lightly floured surface with floured rolling pin, roll each dough round into 6-inch circle. Spoon 1/4 cup filling into one side of each dough round. Brush edges of dough with beaten egg. Fold dough over to cover filling; seal with fork.
Place turnovers on baking sheet; brush with egg. Cut small slit in top of each turnover. Bake 15 minutes or until golden brown. Cool slightly; serve warm.