Preheat the oven to 350°F. Line an 18 x 13-inch rimmed baking sheet with parchment paper.
Add the softened butter, vegetable oil, granulated sugar, and powdered sugar to a large mixing bowl. Beat until smooth and creamy.
Add the milk and eggs. Mix until well combined.
In a separate bowl, whisk together the baking powder, cream of tartar, salt, and all-purpose flour.
Gradually add the dry ingredients to the wet ingredients. Mix just until combined. Do not overmix.
Transfer the cookie dough to the prepared baking sheet. Press and spread the dough evenly to the edges of the pan.
Bake for 13 to 15 minutes. The edges should be lightly golden while the center remains pale. A toothpick inserted into the center should come out without raw batter.
Remove from the oven and allow the cookie bars to cool completely before frosting.
To make the frosting, add the softened butter and sour cream to a large mixing bowl. Beat until smooth and creamy.
Add the vanilla extract and mix until combined.
Gradually add the powdered sugar and orange gel food coloring. Mix until smooth and evenly colored.
Add the milk, 1 tablespoon at a time, until the frosting reaches a smooth, spreadable consistency. Add additional orange food coloring as needed.
Spread the frosting evenly over the completely cooled cookie bars.
Immediately top with Halloween sprinkles.
Refrigerate until the frosting is set and the bars are ready to serve.
Cut into 24 squares and serve.