Preheat the oven to 350°F (177°C) and line two baking sheets with parchment paper.
In a large bowl, cream butter, cream cheese, granulated sugar, and brown sugar until light and fluffy, about 2 minutes.
Add the egg and vanilla extract, beating until just combined, about 30 seconds.
In a separate bowl, whisk flour, cocoa powder, baking soda, and salt.
Gradually add dry ingredients to the wet mixture and mix on low until just combined.
Using a 2-tablespoon scoop, portion the dough and roll into balls.
Flatten each ball into a disk and pipe 1 teaspoon of chilled filling into the center.
Top with another dough disk, seal edges, and gently roll into a smooth ball.
Arrange cookies 2 inches apart on prepared sheets.
Bake for 10 to 12 minutes, until cookies are set around the edges.
Allow cookies to rest on baking sheets for 2 minutes before transferring to a wire rack to cool completely.