Using a stand mixer fitted with a paddle attachment beat together butter and sugars over medium-high speed until light and fluffy, about 2 minutes. Add the egg and beat for about 2 more minutes. Add the vanilla and mix until just combined.
1 cup unsalted butter, 1 large egg, 1 teaspoon vanilla extract
Reduce the speed to low and add the flour mixture, beating just until evenly combined. If you have to, use a wooden spoon or rubber spatula to combine any remaining flour.
Lay 2 large pieces of parchment paper on a clean work surface and put half of the dough along the center of each piece. Shape the dough into 2 logs measuring about 1 1/2-inches in diameter and 10-inches long. Roll logs up in the parchment and refrigerate for at least 1 hour.
Preheat oven to 350 F and position rack in the center of the oven.
Cut the logs into 1/2-inch slices. Roll the edges of the cookies in sugar to coat and shake off excess. Arrange on a baking sheet, leaving 1/2-inch between the cookies.
Bake until set and golden on the edges, about 13 to 18 minutes. Place parchment paper underneath wire cooling racks, then transfer the cookies to the racks to cool completely.
For the Chocolate Dip
Place the chopped chocolate and shortening in a glass or metal bowl and place it over a pot of simmering water (about an inch or so of water). The bowl should not touch the water.
Stir chocolate and shortening with a rubber spatula until smooth. Dip half of each cookie into the chocolate, shake off excess, and set on a cooling rack. Now is the time to add optional garnishes such as extra orange zest or toasted coconut.
Allow the chocolate dipped cookies to harden at room temperature. If you are short on time, you can pop them in the refrigerator for at least 15 minutes to help them set up quickly.
You'll need about 1 large orange or 2 medium oranges to yield 2 tablespoons of packed orange zest. Use a microplane grater to get a good zest. Don't zest too far into the pith, otherwise it will be bitter.
A bar of baking chocolate is best for dipping, though candy melts will work as well. I wouldn’t suggest using chocolate chips, it thickens up too much and is difficult to dip in.
Take your butter out of the fridge about 20 minutes before beginning, or while you prep your other ingredients. Cut it into thin slices and allow it to rest on the counter. Your butter should leave a slight indent when gently poked. That's how you know when it's room temperature (AKA softened).
Weighing your flour with a kitchen scale is the absolute best course of action when it comes to baking goodies. If you don't own a scale, use the scoop and sweep method. Scoop the flour into a measuring cup using a spoon until overflowing. Gently level the top with the back end of a butter knife. Too much flour can equal crumbly, dry cookies, whereas too little flour will cause your cookies to spread overly thin.