To a stand mixer fitted with a paddle attachment, add softened butter, powdered sugar, softened butter, and vanilla. Set speed at 2, and mix together, scraping down the sides of the stand mixer as you go. Once combined, add in the egg and continue to mix. Set aside.
In a separate bowl, combine flours, salt, baking soda, and baking powder.
Add the dry mixture into the wet stand mixture, mixing on low speed until all combined.
Transfer the dough into a bowl, cover with plastic wrap and place in the freezer for 15 minutes, or the refrigerator for an hour (but no longer than 24 hours.)
While dough is firming up, clean stand mixer and use the whisk attachment to make the frosting. Add the cream cheese, powdered sugar, vanilla, and salt to the mixer bowl. Mix on low until combined. Frosting should be thick, but spreadable. Add an extra splash of milk if necessary. Place in refrigerator until ready to frost cookies.
Remove dough from freezer and preheat oven to 375 degrees F. On a flat cutting board or marble countertop, sprinkle flour to coat and create a nonstick surface. Portion the dough into 4 portions and gently press one dough ball at a time onto the surface in the flour. Use a rolling pin to create an even sheet of dough, and if necessary, flip. Do not roll to thin, these cookies are best thick!
Using your favorite cut-outs, press into dough. Continue until 6 to 8 cookies are formed per ball. Recipe yields between 24 to 32 depending on how thin (or thick) you keep the dough!
Use a spatula to pick up cut-out cookie dough and place on a baking sheet sprayed with cooking spray or lined with parchment paper.
Place sheets in oven and bake for 8 to 9 minutes, edges should be lightly browned but tops should still be soft to touch.
Remove and let cool on baking sheet for 10 minutes. Frost and enjoy!
Store in an airtight container in the refrigerator for up to 10 days or freeze for up to 3 months.
Notes
Here are a few modifications you can make based on what you may have on hand:
Sub avocado oil butter for your butter sticks you have on hand.
Or, sub for equal portion light cream cheese for a fun, light twist!