In a small bowl, stir together condensed milk and 1/4 cup water.
In a medium bowl, whisk together dry ingredients. Cut or rub in butter until mixture resembles coarse cornmeal.
Stir in milk mixture just until combined. Flatten dough into 2 disks, wrap in plastic wrap, and chill at least 1 hour. "Shaping the dough into a disk helps it chill evenly and quickly. And chilling relaxes the dough so it won't spring back when you're rolling it out."
Preheat oven to 300°. Break dough into marble-size balls (15 g each). Roll in your palms until smooth and dense. On a lightly floured surface, gently roll each ball out into a 1/4- by 10-in. rope (cover remaining balls to keep them moist). Lift onto a parchment-lined baking sheet.
Brush with egg and bake 15 minutes or until golden. Cool completely on a rack.
Meanwhile, put candy canes in a double layer of resealable plastic bags and crush with a rolling pin. Pour onto a plate.
Melt chocolate in a double boiler or metal bowl set over (not in) a pot of simmering water until about half-melted; stir. Transfer to a 9- by 13-in. baking dish. Let cool until it thickly coats a spoon, 10 minutes.
Set dish on counter with the long side facing you. Place a folded dishtowel under one end so chocolate pools at other end. Roll each stick in chocolate to cover 3/4 of cookie. Holding stick over a clean bowl, sprinkle with crushed candy and set out on a sheet of parchment or waxed paper to dry, about 30 minutes. "Don't refrigerate these; they'll get soggy."
Make ahead Dough, up to 3 days chilled or 1 month frozen airtight; baked, up to 3 days airtight at room temperature.
More pockys, please
STAR OF DAVID Halve dough rope. Form 1 rope into a triangle; form another on top. Brush with egg and top with blue or silver sparkling sugar; bake.
CANDY CANE To half the dough, add natural red coloring, such as India Tree. Lay 1 plain dough rope alongside 1 red rope. Roll ends of double rope in opposite directions to twist. Curve into a candy cane; brush with egg; bake.
CHRISTMAS TREE Use slightly larger dough balls for longer ropes. Leaving 1/2 in. for trunk, coil rope into sideways figure eights. Brush with egg, sprinkle with green sparkling sugar, and bake.
Note: Nutritional analysis is per cookie.