In large bowl, beat brown sugar and butter with electric mixer on medium speed until light and fluffy, scraping bowl occasionally. Beat in vanilla and eggs until well blended. On low speed, beat in flour and baking soda until well combined, scraping bowl occasionally. Cover dough with plastic wrap; refrigerate at least 2 hours for easier handling.
Meanwhile, in 2-quart saucepan, mix filling ingredients; heat to boiling. Reduce heat to low; simmer uncovered 10 minutes, stirring frequently. Refrigerate until ready to use (mixture will thicken as it cools).
Heat oven to 375°F. Work with 1/3 of dough at a time; keep remaining dough refrigerated. On well-floured work surface, roll out dough with rolling pin to 1/8-inch thickness. Cut with floured 2 1/2-inch round cookie cutter. In half of cookies, cut out and remove 1-inch round or desired shape of hole from center. Place whole cookies on ungreased cookie sheets.
Spoon 1 teaspoon cooled filling onto center of each whole cookie; top with dough ring. With fingertips or fork, press edges of dough to seal. Return dough centers to remaining dough for rerolling.
Bake 7 to 10 minutes or until light golden brown. Cool 1 minute; remove from cookie sheets.