Make pastry dough: Whisk together flour, baking powder, baking soda, and salt in a bowl.
Pulse butter, cream cheese, yolk, and vanilla in a food processor until smooth, then add flour mixture and pulse until dough just forms a ball.
Halve dough and form each half into a roughly 6- by 2-inch rectangle. Chill, wrapped in plastic wrap, until firm, about 1 1/2 hours.
Make filling: Purée figs, honey, juice, zest, and cinnamon in cleaned food processor until almost smooth.
Make logs: Roll out 1 piece of dough between 2 sheets of wax paper into a 10- by 8-inch rectangle (about 1/3 inch thick), long side facing you. Remove top sheet of wax paper and gently spread one fourth of fig mixture over bottom half of dough, leaving a 1/4-inch border. Using wax paper as an aid, roll dough, jelly-roll style, halfway, enclosing fig mixture. Flip dough, with wax paper. Remove paper. Spread with one third of remaining fig mixture and roll in same manner, to form an S-shaped log. Make another log. Chill logs, wrapped in wax paper, until firm, at least 4 hours.
Bake cookies: Put oven rack in middle position and preheat oven to 375°F.
Cut logs crosswise into 1/3-inch-thick slices and arrange slices about 2 inches apart on lightly buttered baking sheets. Bake until pastry is pale golden, 12 to 15 minutes. Transfer to racks to cool.
Unbaked logs can be chilled up to 3 days.
Keep cookies layered between sheets of wax paper or parchment, in an airtight container at room temperature for up to 1 week.