Surprise your guests with a cookie appetizer! Pair it with a cocktail and you'll look like a genius. The dough can be made ahead, rolled out between wax or parchment paper, and frozen so you all you have to do is bake them for your big day.
Remove the thyme leaves from the stalk and chop the thyme finely.
Zest the orange using a microplane grater, if you have one.
In a small bowl, rub the thyme and zest into the sugar until the sugar is moist and aromatic.
In a standing mixer fitted with the paddle, beat the butter with the orange thyme sugar at low speed until creamy. Beat in the egg yolk until just combined, about 1 minute. Slowly drizzle in the olive oil and beat until smooth. Add the salt and flour and beat until just incorporated.
Turn the cookie dough out onto a work surface and knead until it just comes together. Divide the dough in half and press each half into a disk. Roll out each disk between 2 sheets of wax paper or parchment to about 1/4 inch thick. Slide the wax paper–covered disks onto a baking sheet and freeze for at least 1 hour, until very firm.
Preheat the oven to 350° and line 2 large baking sheets with parchment paper. Working with one piece of cookie dough at a time, peel off the top sheet of wax paper. Using a 1 1/2-inch round cookie cutter, stamp out the cookies as close together as possible. Arrange the cookies 1 inch apart on the prepared baking sheets.
Bake the cookies for about 20 minutes, until they are lightly golden; shift the baking sheets from top to bottom and front to back halfway through. Let the cookies cool on the baking sheets for 3 minutes, then transfer them to a wire rack to cool completely. (if your dough, as mine was, is a little thinner than 1/4 inch, reduce the cooking time by about half)
MAKE AHEAD — The rolled-out frozen cookie dough can be wrapped in plastic and kept frozen for 2 weeks. The baked cookies can be kept in an airtight container for up to 2 days.