In a heavy 2-quart pan, melt butter over low heat. Stir in cocoa. Add salt, sugar and applesauce. Stir often until mixture comes to a boil.
Remove from heat immediately so it does not caramelize. Add oats and vanilla. If not using nuts, add more oats so cookies hold their shape.
Drop by heaping tablespoons onto wax paper. Allow cookies to cool and dry before storing. If sticky, roll in powdered sugar. Makes 2-3 dozen.