Preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper.

In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.

In a large bowl, use an electric mixer to beat softened butter and granulated sugar together until light and fluffy, about 3 minutes.

Add in the egg and vanilla extract, mixing until fully combined.

Gently fold in the sour cream until the mixture is smooth.

Gradually incorporate the dry ingredients into the wet mixture, mixing on low speed until just combined.

Divide the dough into two portions, wrap each in plastic wrap, and refrigerate for at least 1 hour.

On a floured surface, roll out one portion of dough to about 1/4 inch thickness.

Use cookie cutters to cut out shapes and place them on the prepared baking sheets, about 1 inch apart.

Bake for 8-10 minutes, or until the edges are set but the centers remain soft.

Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to wire racks for complete cooling.

Repeat the process with the remaining dough.