In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, vanilla, granulated sugar, and brown sugar on medium-high speed until fluffy and slightly lighter in color, about 3-5 minutes. Scrape down the sides of the bowl with a rubber spatula.
While the butter and sugar are mixing, combine the flour, salt, and orange zest in a medium bowl with a fork, stirring well, so that the zest is broken up and coated in the flour. (This will keep the zest from sticking to itself and clumping!)
Add the flour mixture to the butter mixture a little at a time, mixing on low speed, until just combined.
Prepare two large pieces of cling wrap. Turn out the dough onto a clean surface and divide in half. Place each half on a piece of cling wrap, then fold the wrap over the dough and roll the dough into logs, about 2 inches in diameter. Refrigerate 2 hours (or freeze 1 hour if you’re in a hurry!)
Preheat the oven to 350F. Line two large baking sheets with parchment paper and remove the dough from the refrigerator. Unwrap and slice the dough logs into half-inch thick rounds, and arrange 1 inch apart on the baking sheets. Bake 12-15 minutes, or until golden and just starting to brown on the edges. Remove from the oven and let cool.
Meanwhile, melt the chocolate in the microwave in 20 second increments (stirring between), or in a double boiler over medium-low heat. When the cookies are cool enough to handle, dip each into the chocolate in a scooping motion so that half of the cookie is covered, then place back on the parchment paper to set. If you’re in a warm environment, set and store cookies in the refrigerator. Enjoy!