Line a baking sheet with parchment, and put about ⅓ cup sugar in a shallow bowl. Set aside.
Preheat oven to 350 degrees F.
Fix KitchenAid with paddle attachment (You can also use a hand mixer) and mix butter 20-30 seconds until soft.
Add oil and mix about a minute. Depending on how soft the butter is, it might all come together or you could have some pieces of butter - that is OK.
Add egg, sour cream, sugar, and almond and vanilla extracts.
Mix on low-medium until well combined.
Add flour, baking powder, and salt. ***To measure flour, stir, scoop into a measuring cup, and level off with the flat side of a knife.
Mix just until the dough comes together and is smooth and everything is combined.
Scoop generous about 2 tablespoons of dough onto prepared cookie sheet, keeping the cookies 2-3 inches apart.
Spray the bottom of a glass or jar with cooking spray before dipping in sugar for the first time (so the sugar sticks to the bottom of the glass).
Press the glass down on a cookie while twisting slightly (this will give the cookies the classic jagged edge). The glass should make a slight indent in the center of the cookie.
Repeat with remaining balls of dough on the cookie sheet, then bake for 8-9 minutes. The cookies will not brown, and should be slightly soft to the touch but not doughy.
Allow the cookies to cool on the baking sheet for a few minutes, then remove to a wire rack. Allow all cookies to cool completely before frosting.