Preheat oven to 350°F.
In mixer, beat butter and 2/3 cup sugar on medium speed about 1 minute or until smooth.
Add egg yolks, rum extract, water, lemon zest, and vanilla. Mix on high speed, beat about 1 minute or until blended.
In medium bowl, stir together flour, baking powder and salt. Stir flour mixture into butter mixture until well blended.
Cover; refrigerate 30 minutes.
Shape dough into 3/4-inch balls and place on parchment lined baking sheet.
Dip bottom of small glass into 1/4 cup sugar; press on cookies to make about 1 1/2 inches in diameter.
Bake 10 to 11 minutes or just until edges begin to brown. Remove from cookie sheets to cooling rack. Cool completely.
Make sandwich cookies by placing 1 tablespoon of caramel in between 2 cookies.
Serve or store in an airtight container in the refrigerator