Begin by preheating your oven to 375 degrees F. In a large bowl, beat together the butter, oil, sugar, and confectioners' sugar using a hand or stand mixer. Beat in the eggs one at a time until smooth; then beat in the vanilla.
In a medium bowl, whisk together the flour, baking soda, cream of tartar, and kosher salt. Add all of this to the creamed mixture and mix until almost combined. Then add 2 3/4 cups of the Sour Patch Kids and gently mix to evenly distribute them.
Roll the dough into 1 1/2-inch balls and place them on an ungreased cookie sheet about 2 inches apart. Flatten each ball by pressing it with your hand. If desired, add an extra Sour Patch Kid to the top of each cookie.
Bake 8-10 minutes until lightly browned. Place cookies on wire racks to cool. Pack and store in an airtight container.
*I used the heart-shaped candies for Valentine's Day, but any variety will work.
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