Preheat oven to 350F°, prepare cookie sheets using parchment paper or a silicon baking mat.
In a large bowl cream together the butter and cream cheese until no lumps are found. Next add the brown sugar, granulated sugar, egg, vanilla extract, and mix until light and fluffy. Set this bowl aside.
In a medium size bowl, whisk together the all purpose flour, baking soda, and salt. Add the dry ingredients into the wet ingredients and mix until well combined.
Separate the cookie dough into 3 bowls, add the pocky sticks, and mix.
Using a cookie scooper, place onto the baking mat and bake for 8-9 minutes.