1. To prepare filling, drain pineapple in a fine-mesh sieve, pressing solids; reserve juice for another use. Place pineapple in a medium saucepan over medium-low heat; cook 15 minutes or until liquid evaporates, stirring frequently. Add granulated sugar and 1/4 teaspoon salt; cook 10 minutes or until liquid mostly evaporates, stirring occasionally. Add corn syrup; cook 5 minutes or until mixture is thick and sticky, stirring frequently. Add all-purpose flour; cook 1 minute or until very thick, stirring constantly. Scrape mixture onto a baking sheet, and spread into a thin layer; cover and chill completely (about 20 minutes).
2. To prepare shortbread, sift dry milk into a bowl. Weigh or lightly spoon cake flour into dry measuring cups; level with a knife. Sift together dry milk, cake flour, 1/4 teaspoon salt, and baking powder. Place butter in a large bowl; beat with a mixer at medium speed until smooth and creamy. Add 1/2 cup powdered sugar; beat 2 minutes or until well combined. Add egg yolks, 1 at a time, beating well after each addition. Beat 2 minutes or until fluffy. Add flour mixture; beat at low speed just until combined. Divide dough in half. Gently shape dough into 2 (10-inch) logs; cover with plastic wrap. Chill 30 minutes.
3. Arrange 1 oven rack 2 positions down from the top of oven; arrange another rack 2 positions up from bottom of oven. Preheat oven to 325°.
4. Cut each dough log into 12 equal pieces. Working with 1 piece at a time, roll dough into a 3-inch circle on a lightly floured surface. Place about 1 tablespoon filling in the center; bring edges together over filling, and pinch closed. Gently press into a floured 1 3/4-inch square mold or cookie cutter, or shape into a square shape by hand. Place cake on a parchment-lined baking sheet. Repeat procedure with remaining dough and filling, placing cakes 2 inches apart on 2 parchment-lined baking sheets (12 cakes per sheet). Bake at 325° for 25 minutes, turning cakes over and rotating pans after 15 minutes. Remove cakes from pans, and cool completely on wire racks. Sprinkle with 1 tablespoon powdered sugar, if desired.