In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar, granulated sugar, and salt. Beat until light and fluffy, scraping side of bowl often. Add egg, lemon peel, almond extract, and rum extract; beat well.

Add the 1/3 cup finely ground almonds; beat well. Beat or stir in flour. Divide dough into three portions. Cover and chill about 2 hours or until dough is easy to handle.

Preheat oven to 350 degrees F. Lightly grease a cookie sheet; set aside. On a lightly powdered-sugared surface, roll out one of the dough portions to an 1/8-inch thickness. Using a fluted square or round 1-1/2- to 2-1/2-inch cookie cutter, cut out dough. Place dough squares or rounds 1 inch apart on prepared cookie sheet. Bake in preheated oven for 8 to 10 minutes or until tops are a very pale golden brown. Carefully transfer cookies to a wire rack; let cool. Repeat with remaining dough portions.

Spread about 1 tablespoon of the dulce de leche on the bottom of each of half of the cookies. Top with remaining cookies, flat sides down, pressing lightly together. If desired, sprinkle tops of assembled sandwich cookies with finely ground toasted almonds. Makes about 24 sandwich cookies.

Dulce de leche is a caramelized milk product that's used in Hispanic cooking. Look for it in the ethnic foods section of larger supermarkets or at Hispanic food stores.

Layer unfilled cookies between waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months. To serve, thaw cookies if frozen. Assemble sandwich cookies as directed in step 4.