In the bowl of a food processor, combine flour, salt, and cayenne and pulse twice to mix.
Add the butter and pulse until the mixture resembles coarse meal, about 10 pulses.
Add the cheese and pulse twice to combine. With the motor running, pour in the cream and continue processing until the dough forms a single mass.
Transfer the dough to a work surface and roll into a log about 2 inches in diameter. Wrap with plastic wrap and refrigerate for at least 3 hours or up to 2 days.
Preheat oven to 325°F Line a baking sheet with parchment paper.
Cut the dough into 1/8 inch thick slices and place on the prepared baking sheet. If desired, using miniature decorative cutters, cut out the center of each slice, then place the cutouts on the baking sheet.
Bake until the crackers are light golden brown, about 20 to 25 minutes.
Transfer the baking sheet to a wire rack. When the crackers are cool to the touch, transfer them to the rack.
Store in an airtight container at room temperature.
Tip: Prepare the dough, shape into logs and refrigerate for up to 2 days before baking. If desired, bake the crackers up to 2 days in advance.