Pulse pecorino in the bowl of a food processor until cheese is pebbly, then transfer to a small bowl and set aside. Add olives to food processor and pulse until coarsely chopped. Transfer to bowl with cheese.

Wipe out food processor, then add flour, sugar, and salt and pulse to combine. Add butter, a few chunks at a time, and pulse until flour mixture and butter start to come together. Add cheese, olives, and fennel seeds and pulse again.

Sprinkle dough with ice water, 1 tablespoon at a time, pulsing between additions, until dough starts to pull away from sides of bowl in a mass. Remove dough from food processor, gather into a ball, and divide in half. Shape each half into a disk, wrap each disk tightly in plastic wrap, and refrigerate for at least 1 hour or up to 3 days.

Arrange a rack in center of oven and heat oven to 350°F. Line 2 baking sheets with silicone liners or parchment paper. Flour a work surface and remove dough from refrigerator. Working with 1 disk at a time, unwrap and roll out into a ¼-inch-thick round.

Use a 2-inch-wide round cookie cutter to stamp out dough (reroll scraps just once). Place rounds on prepared baking sheets and bake for 15 to 18 minutes, until fragrant and golden brown. Let cookies cool on baking sheets for a couple of minutes, then transfer to a rack to cool completely before serving.