This savory Southern hors d'oeuvre can be made up to a week in advance, giving you more time to enjoy your guests on Thanksgiving Day.
Place cheese, butter, flour, salt, and cayenne pepper in the bowl of a food processor; process until a dough is formed, about 10 seconds. Turn dough out onto work surface and divide into two equal pieces. Roll each piece of dough into a 1 1/2-inch-thick log; wrap with wax or parchment paper and refrigerate until dough is firm, at least 2 hours and up to overnight.
Preheat oven to 350 degrees. Line two baking sheets with parchment paper; set aside.
Unwrap dough and slice each log crosswise into 1/4-inch-thick rounds. Place dough rounds on prepared baking sheet 1 1/2 inches apart; gently press a pecan half into the center of each. Brush with egg whites and sprinkle lightly with paprika.
Bake biscuits until crisp, about 15 minutes. Let cool for 5 minutes on baking sheets before transferring to a wire rack to cool slightly. Serve warm or at room temperature.
Biscuits may be kept in an airtight container for up to 1 week.