Sift flour, cornstarch, and cocoa powder together into a bowl. In a large mixing bowl beat the butter, olive oil, sugar, salt, and pepper with an electric mixer about 2 minutes or until smooth. Add yolk; beat for another minute, scraping down bowl as needed. Add dry ingredients all at once, beating on low speed until you have moist curds. (After a minute or two of mixing, you might get discouraged the dough will look dry and shaggy but keep mixing, and it will moisten. You are done mixing when you can squeeze some of the curds and they hold together easily.) Using a flexible spatula, stir in the olives.
Turn dough out, and knead briefly to bring it together; divide in half. Roll each half into an 8- to 81/2-inch log. Wrap with plastic wrap; refrigerate for at least 2 hours or freeze for at least 1 hour.
Position racks to divide oven in thirds; preheat to 325 degrees F. Line two baking sheets with parchment paper. Working with one log at a time, use a thin sharp knife to cut dough into 1/4-inch-thick slices. Place the slices an inch apart on the prepared baking sheets.
Bake cookies for 15 to 17 minutes (rotate baking sheets top to bottom and front to back after 8 minutes) or until just firm to the touch. Let cool on baking sheets 3 minutes. (They are fragile when warm, so don't lift them until they've cooled a bit.) Carefully transfer to wire racks to cool.