Position a rack in the upper third of the oven and crank up the heat to 375°F (190°C). Cut 3 pieces of parchment paper cut to fit your baking sheet.
Stir together the flour, olives, sugar, baking powder, lemon zest, cinnamon, and salt in a medium bowl. Whisk together the oil and egg, pour the mixture into the dry ingredients, and mix with your hands until the dough no longer looks dry and holds together when squeezed, 1 to 2 minutes.
Fill a small bowl with sugar and set nearby. Pinch off 1 rounded tablespoon (about 1 ounce) of dough, roll it into a ball, and coat it well with sugar. Place the parchment paper on your work surface and place the dough ball near one corner of the parchment. Place another piece of parchment on top and, using a rolling pin, roll the ball into a 3 1/2- to 4-inch circle that's a scant 1/16 inch thick. The edges of the cookie will be ragged; that's how it should be. Repeat with 4 or 5 more wafers on the same sheet. Lift off the top sheet of parchment and slip the parchment with the cookies onto the baking sheet.
Bake until the lemon-olive cookies are edged with brown and pebbled on top, 10 to 12 minutes. Slide the parchment onto a wire cooling rack. Repeat with the remaining dough, using a new piece of parchment for each. Once cooled, the cookies will keep in an airtight container for several days, but I doubt they'll stick around that long.