Combine the first 5 ingredients in a medium saucepan. Bring to a simmer over medium heat, stirring frequently, and cook until thick and bubbly (about 2 minutes). Remove from heat; stir in the butter and vanilla. Pour into a bowl; cover surface of pudding with plastic wrap, and chill. Remove plastic wrap, and fold in 1 cup whipped topping.
Split ladyfingers in half lengthwise. Line each of 8 parfait glasses with 4 ladyfinger halves, standing the halves upright. Spoon 2 tablespoons pudding into the center of each glass, and top each portion with 2 teaspoons cookie crumbs. Spoon 1/4 cup pudding on top of crumbs. Top each parfait with 1 tablespoon whipped topping, and sprinkle each serving with 1 teaspoon crumbs.