Add the butter, powdered sugar, and vanilla to a large bowl. Beat with an electric hand mixer on low speed until smooth and creamy.
Add the eggs 1 at a time and beat on medium speed to incorporate, scraping down the sides of the bowl with a spatula halfway through.
Add the salt and incorporate the flour in 3 additions, scraping down the sides of the bowl as needed, until a dough forms.
Turn the dough out onto a clean, floured surface and form into a ball. Cut the ball of dough in half. Cut one of the halves in half, and the other half into thirds, so you have 5 pieces total. Take one of the larger pieces and cover the rest with plastic wrap so they don’t dry out.
Wearing gloves, add the yellow food coloring and knead into the dough until fully incorporated. Cover and set aside each piece of dough after working the color in. Dye the other large piece with red food coloring. Set aside one of the smaller pieces to remain plain. Remove a 1-tablespoon chunk from 1 of the 2 remaining pieces and dye with black food coloring. Dye the rest of that piece blue. Dye the remaining piece of dough green.
Roll out 1 tablespoon of the the plain dough into a 6-inch-long (15-cm) rope. Roll the rest into a 6-inch-long (15-cm) log and cut crosswise into thirds. Shape the logs into 6-inch-long (15-cm) triangle wedges.
Roll a third of the red dough into a 6-inch-long (15-cm) triangle wedge.
Roll the blue piece into a 6-inch-long (15-cm) triangle wedge. Roll half of the green dough into a 6-inch-long (15-cm) triangle wedge.
Form a beach ball shape by placing the plain rope in the middle and alternating the plain dough triangle wedges with the colored triangle wedges. Roll together to fuse, then wrap tightly in plastic wrap and chill in the refrigerator for 30 minutes while you assemble the other shape.
Roll the remaining red dough into a 6-inch-long (15-cm) log, then shape into a triangle wedge.
Roll the remaining green dough into a 6-inch-long (15-cm) log, then flatten.
Place the red triangle on top and trim the edges with a bench scraper or knife.
Cut the yellow dough in half. Set aside one half, then cut the other half in half again and roll into 2 6-inch-long (15-cm) logs and flatten slightly. Place the yellow pieces over each exposed side of the red dough, then pinch the yellow and green dough together to completely cover the red. Roll together to fuse, then wrap tightly in plastic wrap and chill in the refrigerator for 30 minutes.
Use a ruler and a knife to score ¼-inch (6 mm) marks across both chilled logs. Cut into slices with a sharp knife, cleaning the knife after each slice, if necessary.
Roll out the rest of the yellow dough to make a 6-inch (15-cm) by 12-inch (30-cm) rectangle.
Build a single dough log by stacking alternating strawberry slices and beach ball slices over the center of the yellow dough. Wrap the yellow dough around the log, roll together to fuse, then wrap tightly in plastic wrap and chill in the refrigerator for 30 minutes.
Preheat the oven to 300˚F (150˚C). Line a baking sheet with parchment paper.
Use a ruler and a knife to score ¼-inch (6 mm) marks across the chilled dough. Cut into slices with a sharp knife, cleaning the knife after each slice, if necessary. Each slice should have a beach ball side and a strawberry side.
Set the cookies on the prepared baking sheet, strawberry-side up. Break off tiny pieces of the black dough, roll into seeds, and press onto the strawberries.
Bake the cookies for 10-12 minutes, or just until they begin to start turning golden brown. Cool on a wire rack for 5-10 minutes before serving.