For dough, combine flour, sugar, baking powder, baking soda, cinnamon and salt. Cut in butter until dough is a rough, crumbly texture. Add whole egg and egg yolk and blend in until dough comes together. Shape into a disc, wrap and chill for an hour.
For filling, combine all ingredients in a small saucepot and bring up to a simmer. Simmer until the figs absorb all liquid, about 10 minutes. Let cool and purée in a food processor and chill completely.
Preheat oven to 375 °F. On a lightly floured surface, roll out dough into a rectangle, just under ¼-inch thick. Using a knife or pastry cutter, cut strips of dough that are at least 4 ½ inches wide. Spoon filling (or pipe with a piping bag) along center of the strip. Brush left side of pastry dough with egg wash and fold right side of pastry over filling, so that egg washed side meets it. Trim edges. Lift filled cookie tube to a parchment-lined baking sheet and press down to flatten. Repeat with remaining strips and brush tops with egg wash. Bake for 15 to 18 minutes, until a light golden brown. Allow cookies to cool, then cut strips into 1-inch bites.