Pre-heat oven to 375°F and line a few baking sheets with parchment paper. (I bake them at 350°F in a convection oven)
In a large bowl, whisk together the flour, baking soda, and cream of tartar. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, oil, and sugars on medium-high speed until light and fluffy, scraping the sides as necessary.
Reduce speed to medium and add the eggs, one at a time, mixing just until combined.
Add the vanilla and mix until combined.
Reduce speed to low and add the flour in three additions, scraping down the sides as necessary.
In a medium bowl, beat cream cheese until smooth. (You can do this with a handheld mixer or in the clean bowl of your stand mixer.) Add in the confectioners' sugar, orange extract, orange juice, and food coloring, beating until well combined.
Scoop out 1/4 cup of dough for each cookie, dividing dough ball in half.
Flatten the bottom half of the cookie in your hand, then put a teaspoon or two of the orange cream cheese in the center. (You can fill them with up to a tablespoon of filling, just make sure the edges of the cookie dough can seal.)
Place the top half of the dough over the filling, sealing the edges. Be sure to shape each cookie like a hockey puck so the edges do not burn.
Bake for 15-17 minutes.
Let cool on baking sheet before serving.