Place the grated cheese, flour, butter, egg, pepper, and cayenne pepper in the bowl of a food processor fitted with a steel blade. Process until the mixture starts to form a ball. Wrap the dough in plastic wrap and refrigerate for 30 minutes.

In the bowl of a food processor fitted with a steel blade, combine the olives, pine nuts, and garlic. Pulse several times to chop roughly. Add the olive oil and process until almost smooth. Place in a small mixing bowl, cover with plastic wrap, and refrigerate until ready to use.

Preheat the oven to 400°F. Line two baking sheets with parchment paper or silicone baking mats.

Shape the dough into 1½-inch balls and place on the prepared baking sheets, spacing at least 1 inch apart. Bake for 5 minutes. Remove the pans from the oven but keep the oven on.

Press your thumb into the center of each ball, creating an indentation. Fill each indentation with a small spoonful of the olive mixture. Bake for 5-7 minutes or until the cookies are firm. Serve warm or cooled.