Put the butter in the work bowl of a food processor fitted with the metal blade and process, scraping down the sides of the bowl as needed, until the butter is smooth. Add the sugar and process and scrape until thoroughly blended into the butter. Add the egg and continue to process, scraping the bowl as needed, until the mixture is smooth and satiny. Add the flour all at once, then pulse 10 to 15 times, until the dough forms clumps and curds and looks like streusel.

Turn the dough out onto a work surface and gather it into a ball. Divide the ball in half, shape each half into a disk, and wrap the disks in plastic. If you have the time, chill the disks until they are firm, about 4 hours. If you’re in a hurry, you can roll the dough out immediately; it will be a little stickier, but fine. The dough can be wrapped airtight and refrigerated for up to 4 days or frozen for up to 1 month.

Position the racks to divide the oven into thirds and preheat the oven to 350°F (180°C). Line two baking sheets with parchment paper.

Working with one disk at a time, roll the dough out on a lightly floured surface until it is between 1/8 and 1/4 inch (4 and 7 mm) thick. Using a 1 1/2-inch (4-cm) round cookie cutter, cut out as many cookies as you can and place them on the lined sheets, leaving about 1 inch (2.5 cm) space between them. You can gather the scraps into a disk and chill them, then roll, cut, and bake them later.

Bake the cookies for 8 to 10 minutes, or until they are set but pale. If some of the cookies are thinner than the others, the thin ones may brown around the edges. Transfer the cookies to cooling racks to cool to room temperature.

The cookies can be kept in a tin at room temperature for about 5 days or wrapped airtight and frozen for up to 1 month.