Combine first 4 ingredients in a large bowl; beat at medium speed of a mixer 2 minutes or until light and fluffy. Add egg; beat at high speed 1 minute or until the mixture is very smooth. Combine flour, baking powder, and salt, and add to sugar mixture, beating at low speed just until flour mixture is moist. Divide dough in half, and gently shape each portion into a ball. Wrap dough in plastic wrap, and chill 8 hours or overnight.
Place figs in a food processor, and pulse 6 times or until chopped. With processor on, slowly add 3 tablespoons sugar, water, corn syrup, and lemon juice through food chute, and process until smooth, scraping sides of processor bowl twice. Spoon the fig mixture into a bowl; cover and chill 8 hours or overnight.
Shape each ball of dough into a 10-inch log. Remove plastic wrap; cut each log into 10 (1-inch) slices. Quickly shape slices into 20 balls; place on a tray lined with wax paper. Chill 30 minutes.
Preheat oven to 400°.
Place each ball of dough between 2 sheets of wax paper, and flatten to a 3 1/2-inch circle. Spoon 1 level tablespoon fig mixture into the center of each circle. With floured hands, fold dough over filling to form a triangle, and pinch edges together to seal. Place triangles 2 inches apart on baking sheets coated with cooking spray, and bake at 400° for 10 minutes or until pastries are lightly browned. Remove from pans, and cool on a wire rack.