Line cookie sheet with waxed paper. Spoon 9 heaping teaspoons dulce de leche on cookie sheet. Place cookie sheet in freezer 1 hour. Transfer remaining dulce de leche to covered container, and refrigerate for another use.
Heat oven to 350°F. Lightly grease or spray cookie sheet. In large bowl, break up cookie dough. Stir or knead in flour until well combined. Form dough into 9 balls. Flatten each ball into 2-inch round; place 1 frozen dulce de leche dollop on center of each round. Shape dough around dulce de leche, sealing to cover completely. In small bowl, mix sugar and apple pie spice. Roll each ball in sugar mixture. Place 1 inch apart on cookie sheet.
Bake 18 to 20 minutes or until edges are golden brown. Cool 3 minutes; remove from cookie sheet to cooling rack.