In a sizable mixing bowl, cream the softened butter and sugar together until the mixture becomes light and airy. Add in the egg and almond extract, blending thoroughly. In a separate bowl, combine flour, salt, and baking powder; gradually incorporate these dry ingredients into the creamed mixture, mixing until a cohesive dough forms.

Set aside 1 cup of the prepared dough. To the remaining dough, add enough red food coloring to achieve a deep red hue. Shape the colored dough into a 3-1/2-inch-long log, wrap it in plastic wrap, and place it in the refrigerator to chill until firm, approximately 2 hours.

Divide the reserved dough into two equal portions. Color one portion with green food coloring, kneading until evenly tinted, and leave the other portion plain. Wrap each piece individually in plastic wrap and refrigerate until firm, about 1 hour.

On a floured surface lined with waxed paper, roll the plain (white) dough into a rectangle, roughly 8-1/2 by 3-1/2 inches. Place the red dough log along the short end of the rectangle, rolling the white dough around it to enclose the red log fully. Set aside.

Roll the green dough on a floured waxed paper surface into a 10 by 3-1/2-inch rectangle. Position the red and white dough log along the short end of the green dough and roll the green dough around the log, encasing it completely. Tightly cover the dough log with plastic wrap and refrigerate for a minimum of 8 hours or overnight for best results.

Preheat the oven to 375°F. Unwrap the chilled dough log and slice into 1/8-inch-thick rounds. Arrange the slices on ungreased baking sheets, spacing them about 1 inch apart. Gently press a few miniature chocolate chips into each slice to mimic watermelon seeds; sesame seeds may also be added if desired.

Bake in the preheated oven for 6 to 8 minutes or until the cookies are firm but have not begun to brown. While the cookies are still warm, cut each round into halves or wedge shapes. Transfer cookies to wire racks to cool fully before serving.