In a large bowl or stand mixer, beat the softened butter and sugar together on medium speed until light and fluffy, about 3 minutes. Add the egg and vanilla extract, mixing until just combined.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the butter mixture on low speed, mixing until a soft dough forms. If dough is too sticky, add 1 tablespoon more flour.
Remove about one-third of the dough and place it in a separate bowl. Add food coloring to this portion and knead until the color is evenly distributed throughout.
Roll the colored dough between two sheets of parchment paper until ½-inch thick. Place in the freezer for 20 minutes until firm.
Using a small heart-shaped cookie cutter (about 1.5 inches), cut out hearts from the chilled pink dough. Stack the hearts on top of each other to form a log, using a tiny bit of water to help them stick together. Freeze the heart log for 30 minutes until solid.
Take the frozen heart log and press the plain dough around it, working it into all gaps. Roll into a smooth cylinder about 2 inches in diameter. Wrap tightly in plastic wrap and refrigerate for at least 1 hour or up to 3 days.
Preheat oven to 350°F. Line two baking sheets with parchment paper.
Slice the chilled dough log into ¼-inch rounds using a sharp knife. Place cookies 2 inches apart on prepared baking sheets.
Bake for 11-13 minutes until edges are just barely golden. Let cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.