Line 2 half-sheet rimmed baking trays with parchment or silicone baking mats. Set aside.

In a large mixing bowl, whisk all purpose flour, baking powder, and kosher salt.

In a separate bowl or the bowl of a stand mixer, whip butter on high speed until creamy, about 30 seconds. Add the granulated sugar and mix on high speed until light and fluffy, about 1 minute more. Mix in the eggs, followed by the vanilla bean paste.

Add the dry ingredients in 2 additions and mix on low speed until just combined.

With a kitchen scale, divide the dough into 3 equal portions, about 300 grams each.

Wrap 2 portions in clingfilm/plastic wrap and refrigerate until ready to use.

Divide the remaining portion into 6 smaller balls, about 50 grams each. Knead in gel food coloring to create red, orange, yellow, green, blue, and purple doughs.

With a sharp chef’s knife, chop all of the colored doughs into small pieces.*

On a sheet of baking parchment, arrange the rainbow dough pieces to create a mosaic pattern. Use your fingers to push the pieces together, making sure there are no gaps or holes in the dough.

Top with a second sheet of baking parchment, then use a rolling pin to roll the rainbow dough to 1/4-inch thickness.

Lifting by the edges of the parchment, transfer the rolled dough to a tray. Refrigerate 1 hour, or until firm.

Peel away the top layer of parchment. Use a 1 1/2-inch heart-shaped cutter to cut the rainbow dough.

Push scraps together, re-roll, and cut remaining hearts.

Stack the hearts on top of one another to form a log.** Freeze 30 minutes, or until very firm.

Meanwhile, remove remaining portions of white dough from the refrigerator to soften .

Break 1 portion of white dough into small chunks, and wedge into the crevasses, and around the outside of the frozen heart log.

Wrap with the remaining portion of white dough, forming a log about 6-7 inches long. Roll log on the countertop to smooth.

Roll in rainbow sprinkles or rainbow nonpareils.

Wrap log in clingfilm/plastic wrap and freeze until very firm, at least 1 hour, or overnight.

With a sharp chef’s knife, trim the rough ends of the frozen log, then cut into 1/4-inch thick slices.

Arrange slices on prepared trays. Freeze15 minutes.

Meanwhile, preheat the oven to 325° F / 165° C.

Bake, 1 tray at a time, in preheated oven for 13-15 minutes, or until set and very lightly golden brown.

Cool 10 minutes on trays, then use a flat metal spatula to transfer cookies to a wire rack to cool completely.

Store slice and bake rainbow heart cookies in an airtight container at room temperature for up to 5 days, or freeze for up to 3 months.